6 fluid ounces per day. Express this rate of flow in cubic meters per year.

Answer: -19.35

Step-by-step explanation:

Given positive acute angles a and b such that: [tex]$\sin a = \frac{20}{29}$ and $\cos b = \frac{40}{41}$.[/tex]

We have to determine the value of[tex]$\cos(a - b)$[/tex]

in its simplest form.To find , we use the following identity:[tex]$\cos(a - b) = \cos a \cos b + \sin a \sin b$[/tex]

Here, we know that [tex]$\sin a = \frac{20}{29}$ and $\cos b = \frac{40}{41}$.[/tex]

We need to determineb$Substituting [tex]$\cos b = \frac{40}{41}$, we get:$\sin^2 b = 1 - \left(\frac{40}{41}\right)^2 = \frac{1681 - 1600}{1681} = \frac{81}{1681}$[/tex]

Taking the square root of both sides, we get:[tex]$\sin b = \frac{9}{41}$Now, let's find $\cos a$[/tex] using the identity [tex]$\sin^2 x + \cos^2 x = 1$.$\sin^2 a + \cos^2 a = 1 \[/tex]

Rightarrow [tex]\cos^2 a = 1 - \sin^2 a$[/tex]

Substituting [tex]$\sin a = \frac{20}{29}$[/tex],

we get:[tex]$\cos^2 a = 1 - \left(\frac{20}{29}\right)^2 = \frac{841 - 400}{841} = \frac{441}{841}$[/tex]

Taking the square root of both sides, we get:$\cos a = \frac{21}{29}$

[tex]$\cos a = \frac{21}{29}$[/tex]

Now, substituting the values of[tex]$\sin a$, $\sin b$, $\cos a$ and $\cos b$ in $\cos(a - b) = \cos a \cos b + \sin a \sin b$,[/tex]

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Answer:  the fraction form is 331/500

Step-by-step explanation:

To determine the coordinates of the vertices of the reflected figure, we can use a reflection matrix that represents reflection over the x-axis. The reflection matrix is:

[tex]\sf\:\begin{bmatrix} 1 & 0 \\ 0 & -1 \\ \end{bmatrix} \\[/tex]

Let's apply this reflection matrix to each vertex of the triangle RST to find the coordinates of the reflected vertices:

For vertex R(-3, 7):

[tex]\sf\:\begin{bmatrix} 1 & 0 \\ 0 & -1 \\ \end{bmatrix} \begin{bmatrix} -3 \\ 7 \\ \end{bmatrix} = \begin{bmatrix} -3 \\ -7 \\ \end{bmatrix} \\[/tex]

So the reflected coordinates for vertex R are (-3, -7).

For vertex S(5, 3):

[tex]\sf\:\begin{bmatrix} 1 & 0 \\ 0 & -1 \\ \end{bmatrix} \begin{bmatrix} 5 \\ 3 \\ \end{bmatrix} = \begin{bmatrix} 5 \\ -3 \\ \end{bmatrix} \\[/tex]

So the reflected coordinates for vertex S are (5, -3).

For vertex T(6, -5):

[tex]\sf\:\begin{bmatrix} 1 & 0 \\ 0 & -1 \\ \end{bmatrix}\begin{bmatrix} 6 \\ -5 \\ \end{bmatrix} = \begin{bmatrix} 6 \\ 5 \\ \end{bmatrix} \\[/tex]

So the reflected coordinates for vertex T are (6, 5).

Now, let's graph the pre-image (triangle RST) and the image (reflected triangle) on the same coordinate grid:

Pre-image (Triangle RST):

Image (Reflected Triangle):

You can plot these points on a coordinate grid and connect them to form the triangles.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:

1/16 of the pizza each.

Step-by-step explanation:

1/8 divided by 2 (because you are splitting the slice into two) equals 1/16.

Answer:

10.4cm

Step-by-step explanation:

100-89.6=10.4

The measure of the segment WX is 10.4 cm

The length of the line segment, WY = 100cm

XY = 89.6 cm

The measure of WX =?

The entire line segment :

WY = XY + WX

100cm = 89.6 cm + WX

100cm - 89.6 cm = WX

10.4 cm = WX

Hence, the measure of the segment WX is 10.4 cm

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Answer:

R=[tex]\frac{C}{2p}[/tex]

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

You convert this to y=mx+b and b=y-value. So, the answer is B.

The engineer should take a sample size of approximately 40 to be 95% confident of being in error by only 0.125 minutes.

To calculate the sample size for estimating the cycle time, the engineer can use the formula for continuous data:

E = (zα/2) * (σ / √n)

where:
E is the maximum allowable error (0.125 minutes),
zα/2 is the z-value for a 95% confidence level (which corresponds to a 0.025 alpha level),
σ is the standard deviation (0.4 minutes), and
n is the sample size (unknown).

Rearranging the formula, we have:

n = (zα/2)^2 * (σ^2 / E^2)

Plugging in the given values, we get:

n = (1.96)^2 * (0.4^2 / 0.125^2)

Simplifying the equation, we have:

n ≈ 3.8416 * (0.16 / 0.015625)

n ≈ 3.8416 * 10.24

n ≈ 39.494

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Answer:

14

Step-by-step explanation:

14^2 = 196

or you could do 4^49=196

Answer:

Step-by-step explanation:

Total to spent

Cost of a desktop PC

Cost of a tablet

Cost of desktop PCs and tablets

Required equation

The standard form allows to see numbers of each item and their total price

By solving we gets for 6 hours of service, both Derrick's Dog Sitting and Darlene's Dog Sitting will cost the same.

Given the rates for Derrick's Dog Sitting and Darlene's Dog Sitting as shown in the given image. We need to write and solve an equation to find the number of hours for which Derrick's Dog Sitting $12 plus $5 per hour the total cost will be the same for the two services. We are also required to analyze which dog sitting service is more economical to use if we need 5 hours of service.The cost of Derrick's Dog Sitting can be represented as:

C = 12 + 5h

where C is the total cost for h hours.

The cost of Darlene's Dog Sitting can be represented as:

C = 7h where C is the total cost for h hours.To find the number of hours for which both services cost the same, we can equate both equations.

12 + 5h = 7h

Subtracting 7h from both sides, we get:

12 = 2h

Dividing both sides by 2, we get:h = 6

Therefore, for 6 hours of service, both services will cost the same

Therefore, Derrick's Dog Sitting and Darlene's Dog Sitting will cost the same for 6 hours of service.

From the given information, we know that the cost of Derrick's Dog Sitting is $12 plus $5 per hour and the cost of Darlene's Dog Sitting is $7 per hour. To find the number of hours for which the total cost will be the same for both services, we wrote and solved an equation. The equation was 12 + 5h = 7h. On solving it, we found that the number of hours for which the cost will be the same is 6 hours. Therefore, both services will cost the same for 6 hours of service.Now, we need to analyze which dog sitting service is more economical to use if we need 5 hours of service. We can calculate the cost for 5 hours of service for both services using their respective rates. For Derrick's Dog Sitting, the cost for 5 hours of service will be:

12 + (5 x 5) = $37

For Darlene's Dog Sitting, the cost for 5 hours of service will be:7 x 5 = $35

Therefore, if we need 5 hours of service, Darlene's Dog Sitting will be more economical to use as it will cost $2 less than Derrick's Dog Sitting.

Therefore, we can conclude that for 6 hours of service, both Derrick's Dog Sitting and Darlene's Dog Sitting will cost the same. However, if we need 5 hours of service, Darlene's Dog Sitting will be more economical to use as it will cost $2 less than Derrick's Dog Sitting.

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Without knowing any pricing information for Darlene's Dog Sitting, we can't fully answer the question. However, for Derrick's Dog Sitting the equation representing the cost is C = 12 + 5*H, where C is the total cost, and H is the number of hours.

In order to find the number of hours for which the total cost for both Derrick's and Darlene's dog sitting services is the same, we need to write and solve an equation. Let's denote the total cost using the symbol C, and the number of hours using H.

For Derrick's Dog Sitting, we know the cost is $12 for the initial fee, plus $5 per hour, which results in the following equation: C = 12 + 5*H.

However, we haven't been given the cost structure for Darlene's service, so we can't complete this part of the question without more information.

Regarding your second question, without knowing the cost for Darlene's Dog Sitting, we cannot say which one is more economical for 5 hours of service.

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Answer:

z = -10

Step-by-step explanation:

5/10 = 1/2

1/2 of 10 = 5

Answer:

I think answer is C . 11.43% is the correct answer. so, mark this answer as BRAINLIEST answer.

Thank you ☺️☺️☺️☺️

The percent of the decrease in salary of his new job is 11.43% and this can be determined by using the unitary method.

Given :

Dain's original salary was $70,000 and his salary at his new job is $62,000.

The following steps can be used in order to determine the percent of the decrease in salary of his new job:

Step 1 - The unitary method can be used in order to determine the percent of the decrease in salary of his new job.

Step 2 - According to the given data, the original salary is $70000 which is 100%.

Step 3 - Let the percentage of the value $62000 be 'x'.

Step 4 - So, the value of 'x' can be calculated as:

[tex]x = \dfrac{62000}{70000}\times 100[/tex]

Step 5 - Simplify the above expression.

[tex]x = \dfrac{620}{7}[/tex]

[tex]x = 88.57[/tex]

Step 6 - So, the percent of the decrease in salary of his new job is:

Percent Decrease = 100 - 88.57

Percent Decrease = 11.43%

Therefore, the correct option is C) 11.43%.

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Answer:

t = 2

Step-by-step explanation:

5t - 4 = 6

make t the subject

move -4 to the other side of the equal sign

5t = 6 + 4

5t = 10

t = 10/5

t = 2

Answer:

t=2

Step-by-step explanation:

5t=6+4

5t=10

t=2

Answer:

Have you tried to do x+6+4x-21=180

combine the like terms and then solve for 180 so (x+4x)(6-21)=180

5x-15=180

    +15  +15

5x=195

5x/5=195/5

x=39

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

3n+14=-4

-14. -14

3n=-18

1/3×-18/1

Answer:

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(5,-11) and (-9, 17)

We have

[tex]m = \frac{17 - - 11}{ - 9 - 5} = \frac{28}{ - 14} = - \frac{28}{14} = - 2 \\ [/tex]

We have the final answer as

[tex] - 2 \\ [/tex]

Hope this helps you

Answer:

2)vertical angles

3)alternate interior angles

Step-by-step explanation:

yeah thats all i got

The line p || r as, the alternate interior angle are equal.

The basic qualities listed below make it simple to identify parallel lines.

We have to prove that p || r

and, we have given <1 = <5

<4 = <1 by (Vertically Opposite Angle).

and, <4 = <5 (Transitive Property)

So, the line p || r as, the alternate interior angle are equal.

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Answer:

See below

Step-by-step explanation:

Equation 1:

Step 1:

6 : 9 = x : 54      Ratio

Step 2:

9x = 324     Multiply

Step 3:

36 small dogs       Divide

Equation 2:

Step 1:

6 : 9 = x : 12       Ratio

Step 2:

9x = 72     Multiply

Step 3:

8 small dogs   Divide

First Answer:

36 small dogs

Second Answer:

8 small dogs

Hope This Helps :)

Answer:

B: 45

Step-by-step explanation:

You can take the first numbers, 3 and 135, and divide them

135/3 = 45

Answer:

M=3+7x+40=4+2x+23

M=3+7x+40-4-2x-23

M=5x+20

M=5x=20

M=5x:5=20:5

M=4

Answer:

I think answer 4, not sure! "Yes, because the transformations taken after the angles...".

Step-by-step explanation:

Answer:

A soft taco costs $1.25 and a burrito costs $2.50

Step-by-step explanation:

To start to find the cost of each, you need to set up a system of equations. Start by using x for the cost of a soft taco. Then use y for the cost of a burrito. First you can compile an equation for what you paid.

3x + 3y = 11.25

Now you can do the same with your friend's purchase.

4x + 2y = 10.00

Now to solve we can use a number of different methods. We'll use elimination this time. To use that, multiply the first equation by -2 and the second equation by 3. Then line them up like this:

-6x - 6y = -22.50

12x + 6y = 30.00

Now we add them straight through to cancel the y's and solve for x.

6x = 7.50

x = 1.25

Now we know the cost of a soft taco is $1.25 and we can find the burrito cost by using the taco cost in either equation.

3x + 3y = 11.25

3(1.25) + 3y = 11.25

3.75 + 3y = 11.25

3y = 7.50

y = 2.50

So we know that a burrito costs $2.50

Different types of integer models refer to different formulations and restrictions applied to the variables in mathematical optimization problems. Here are brief explanations of three commonly used types of integer models: total integer model, 0-1 integer model, and mixed integer model.

1. Total Integer Model: In a total integer model, all variables are required to take integer values. This means that the solution must consist of only whole numbers, without any fractional or decimal values. For example, if a variable represents the number of units to produce, a total integer model would ensure that only whole units can be produced.

2. 0-1 Integer Model: In a 0-1 integer model, the variables are binary and can only take two values: 0 or 1. This formulation is often used for decision variables that represent choices or binary decisions, such as selecting or not selecting a particular option. For example, in a facility location problem, a 0-1 integer variable can represent whether a facility is open (1) or closed (0).

3. Mixed Integer Model: A mixed integer model allows a combination of integer and continuous variables in the optimization problem. Some variables can take fractional or decimal values (continuous), while others must take integer values. This formulation is useful when there is a need to model both discrete decisions and continuous quantities in the same problem. For example, in a production planning problem, the number of machines (integer) and the amount of raw material used (continuous) can be decision variables in a mixed integer model.

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Answer:

Step-by-step explanation:

If the books length (L) is three times as long as the width (W), the equation for area is this:

L · W = 20 inches,

3W · W = 20 inches -  substituting L for 3W

So then the books perimeter is

There are 49.78 grams of fat in the meal consisting of a cheeseburger, large fries, and a chocolate shake.

A meal that comprises of a cheeseburger, large fries, and a chocolate shake contains a total of 1120 kcal. If 40% of total calories in this meal are from fat, how many grams of fat are in this meal?To calculate the grams of fat in the meal, we have to find out the total calories that come from fat, as 40% of the total calories in the meal come from fat.To find out how many calories come from fat, we have to convert the percentage of calories from fat into actual calories. Therefore, we can use the following formula:Fat percentage = (Calories from fat/Total calories) × 100%Let C be the total number of calories in the meal, then the number of calories from fat is given by:Calories from fat = 40% of CUsing this information, we can rewrite the formula as:Fat percentage = (40% of C/C) × 100%We know that the total number of calories in the meal is 1120 kcal, so we can substitute this value in the formula:Fat percentage = (40% of 1120/1120) × 100%Fat percentage = (448/1120) × 100%Fat percentage = 0.4 × 100%Fat percentage = 40%So 40% of 1120 kcal come from fat. To find out how many calories from fat this is, we can use the formula:Calories from fat = 40% of 1120Calories from fat = 0.4 × 1120Calories from fat = 448 kcalTo calculate the number of grams of fat in the meal, we need to convert the number of calories from fat into grams of fat. We can use the following formula:1 g of fat = 9 kcalUsing this information, we can rewrite the formula as:Calories from fat = grams of fat × 9 kcalDividing both sides of the equation by 9 kcal gives:Grams of fat = Calories from fat/9 kcalSubstituting the value of Calories from fat we calculated earlier gives:Grams of fat = 448 kcal/9 kcalGrams of fat = 49.78 g

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a. To calculate the Euclidean distances between the three pairs of facilities, we use the formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2) where (x1, y1) and (x2, y2) are the coordinates of the two points.

Calculating the Euclidean distances:

dAB = sqrt((51 - 27)^2 + (59 - 17)^2) ≈ 45.28 miles

dBC = sqrt((61 - 51)^2 + (66 - 59)^2) ≈ 10.82 miles

dAC = sqrt((61 - 27)^2 + (66 - 17)^2) ≈ 51.23 miles

b. To calculate the rectilinear distances, we use the formula:

d = |x2 - x1| + |y2 - y1|

Calculating the rectilinear distances:

dAB = |51 - 27| + |59 - 17| = 27 + 42 = 69 miles

dBC = |61 - 51| + |66 - 59| = 10 + 7 = 17 miles

dAC = |61 - 27| + |66 - 17| = 34 + 49 = 83 miles

Therefore, the Euclidean distances are approximately dAB = 45.28 miles, dBC = 10.82 miles, and dAC = 51.23 miles. The rectilinear distances are dAB = 69 miles, dBC = 17 miles, and dAC = 83 miles.

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