A bottle of water that is 80°F is placed in a cooler full of ice. The temperature of the water decreases by 0. 5°F every minute. What is the temperature of the water, in degrees Fahrenheit, after 5 1/2
minutes? Express your answer as a decimal

Answer:

C

Step-by-step explanation:

Don't worry about the volume to start with. Just look at the area of the top or bottom.

The hole has a 4 inch diameter

d = 4

r = d/2

r = 2

Area = pi r^2

Area = pi * 2^2

Area = 4 pi

Now find the area of the top (or bottom) if the circle was not there.

L = 8

W = 6

Area = L * W

Area = 8 * 6

Area = 48

Now take away the area of the circle.

Area Top = 48 - 4 * pi

Area Top = 48 - 12.56

Area Top = 35.44

Finally, Find the volume

Volume = area of the top * height

Volume = 35.44 * 15

Volume = 531.6

Answer:

27 students received an A

Step-by-step explanation:

90% of 150 is 135

1/5 of 135 is 27

Tο shift the graph tο the right, we can simply add a pοsitive cοnstant tο the x values οf each pοint befοre plοtting them. Fοr example, if we want tο shift the graph tο the right by 2 units.

The intersectiοn οf twο number lines creates a twο-dimensiοnal plane knοwn as a cοοrdinate plane. The x-axis, a hοrizοntal number line, and the y-axis, a vertical number line, are twο examples οf these number lines.

Tο graph the equatiοn 5x - 3y = 18 οn a cοοrdinate plane, we can fοllοw these steps:

1. Sοlve fοr y in terms οf x:

5x - 3y = 18

-3y = -5x + 18

y = (5/3)x - 6

2. Chοοse sοme values fοr x and use the equatiοn tο find the cοrrespοnding y values. Fοr example, we can chοοse x = 0, 3, and 6:

When x = 0: y = (5/3)(0) - 6 = -6

When x = 3: y = (5/3)(3) - 6 = -3

When x = 6: y = (5/3)(6) - 6 = 2

3. Plοt the pοints (0, -6), (3, -3), and (6, 2) οn the cοοrdinate plane.

4. Draw a straight line passing thrοugh these three pοints. This line represents the graph οf the equatiοn 5x - 3y = 18.

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You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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Answer:

1/5 + 3/5 = 45 = 0.8

Step-by-step explanation:

Spelled result in words is four fifths.

Answer:

63.6%

Step-by-step explanation:

21 out of 33 is what we are working with here. Divide.

21/33

= 0.636363...

Times by 100 to change from a decimal to a percent (you know "per cent" means "per hundred")

= 63.636363...

Round to the nearest tenth as per the instructions.

= 63.6%

These transformations result in the graph of g(x), which is a horizontally reflected, horizontally compressed, horizontally shifted, and vertically shifted version of the parent function f(x) = log(x).

To achieve the graph of g(x) = log("-2x" - 4) - 1 from the parent function f(x) = log(x), several transformations are applied.

First, a horizontal reflection occurs due to the negative coefficient in front of the x term, "-2x". This reflection flips the graph of f(x) across the y-axis.

Next, a horizontal compression takes place due to the coefficient of 2 in "-2x". This compression squeezes the graph horizontally, making it narrower compared to the parent function.

Then, a horizontal shift to the right occurs by 4 units due to the constant term -4. This shift moves the graph horizontally, shifting it to the right.

Lastly, a vertical shift downward by 1 unit takes place due to the constant term -1. This shift moves the entire graph vertically, shifting it downward.

These transformations result in the graph of g(x), which is a horizontally reflected, horizontally compressed, horizontally shifted, and vertically shifted version of the parent function f(x) = log(x).

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The current age of Sam is 30 years and Harry is 10 years.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

Let Sam's age be y years and Harry's age be x years.

Sam is currently three times harry's age.

The equation formed: y = 3x

Sam's age is also 10 more than twice harry's age.

The equation formed: y = 2x + 10

Substitute the value of y from first equation in second equation:

3x = 2x + 10

x = 10

Put the value of x in first equation:

y = 3x = 3*10 = 30

Thus, the current age of Sam is 30 years and Harry is 10 years.

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The average number of intersections the traffic engineer would need for each type of traffic signal to reject the null hypothesis at the 0.01 level of significance with a power of 0.90 is six

To test the effectiveness of these signals, the engineer must reject the null hypothesis, which states that there is no significant difference in the mean delays between the three types of signals. The engineer wants to reject the null hypothesis at the 0.01 level of significance with a power of 0.9. In other words, they want to be 90% sure that they can detect a significant difference if it exists.

Using the data provided in the study, the engineer can calculate the sample size needed for each type of signal. They need at least five intersections for pretimed signals, six intersections for semi-actuated signals, and four intersections for fully actuated signals to reject the null hypothesis at the desired level of significance with a power of 0.9.

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Answer:

you have to right how aed and acd are simaler

Step-by-step explanation:

you should draw the triangle and define the AED and ACD and compare and contrast.

Answer:

52 square units

Step-by-step explanation:

The big area (include red squares) is: \(6\cdot 11=66\) square units

The small area (only red squares) is: \(2\cdot 7=14\) square units

The area shaded in yellow is obtained by subtracting the small area from the big area: \(66-14=52\) square units

This is a table of values of three functions at selected values of x.

It is asking for h(f(-2))

Its saying, take f(-2), and take whatever you get from that and put it into h(x)

So, find f(-2).

Find x = -2, then see what f is there.

f(-2) = -1

So, find h(-1)

h(-1) = 0

Hope this helps :)

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- Jeron

For the two given graphs, the value for vector equation is obtained as \(\vec{w} = 2\vec{u} + \vec{v}\).

What is a vector?

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

From first graph it is seen that -

\(\vec{u}= < 1,1 >\) and \(\vec{v}= < -1,2 >\)

From second graph it is seen that -

\(\vec{w}= < 1,4 >\)

So, it is obtained that -

\(a\vec{v}+b\vec{u}=\vec{w}\)

Substitute all the values in the equation -

a<-1,2> + b<1,1> = <1,4>

<-a,2a> + <b,b> = <1,4>

<-a+b,2a+b> = <1,4>

The two equation obtained are -

-a + b = 1

2a + b = 4

Subtracting the equation 1 from 2 -

2a + b - (-a + b) = 4 - 1

2a + b + a - b = 3

3a = 3

a = 1

Substitute the value of a in equation 1 -

-1 + b = 1

b = 1 + 1

b = 2

So, the equation \(a\vec{v}+b\vec{u}=\vec{w}\) becomes -

\(\vec{v} + 2\vec{u} = \vec{w}\)

Therefore, the vector is obtained as \(\vec{w} = 2\vec{u} + \vec{v}\).

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Answer:

540

Step-by-step explanation:

ARCHITECTURE The Pentagon in Washington, D.C. is shaped like a regular pentagon. Find the sum of the measures of the interior angles of the largest pentagon-shaped section of the Pentagon building. = 180(3) or 540 Simplify. The sum of the measures of the interior angles is 540.

Answer:

896 containers

Step-by-step explanation:

Given that;

1 pint = 1 container

Convert 112 gallons to pint

1 pint x 0.125 gallons

x = 112gallons

Cross multiply

0.125x = 112

x = 112/0.125

x = 896 pints

Since sour cream is sold only in 1-pint containers, then the total container she will buy is 896 containers

The rate of change of y with respect to x when t = 3 is = 3/25 and  the answer is not one of the options given.

An object moves in the xy-plane so that its position at any time tis given by the parametric equations x(t) = t° - 3t + 2 and y (t) = /t² + 16.

To find the rate of change of y with respect to x, we need to find dy/dx, which can be computed using the chain rule of differentiation:

(dy/dt) / (dx/dt) = dy/dx

We first compute dx/dt and dy/dt:

dx/dt = 1 - 3 = -2

dy/dt = 2t / (t² + 16)

When t = 3, we have:

dx/dt = -2

dy/dt = 2(3) / (3² + 16) = 6/25

Therefore, the rate of change of y with respect to x when t = 3 is:

(dy/dt) / (dx/dt) = (6/25) / (-2) = -3/25

So, the answer is not one of the options given.

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Approximately 47.72% of the students scored between 167 and 253 on the exam. To find the percentage of students who scored between 167 and 253 on the exam, we can use the properties of the normal distribution.

Given that the scores are normally distributed with a mean of 253 and a standard deviation of 43, we can calculate the z-scores for the two given scores and then use the z-table to find the corresponding probabilities. First, let's calculate the z-score for the lower score of 167:

z1 = (167 - 253) / 43

z1 ≈ -2

Next, let's calculate the z-score for the upper score of 253:

z2 = (253 - 253) / 43

z2 = 0

Using the z-table, we can find the area under the normal curve between z1 and z2, which represents the percentage of students who scored between 167 and 253 on the exam.

Since the z-score of z1 is -2, we look up the area to the left of -2 in the z-table, which is approximately 0.0228. This represents the percentage of students who scored below 167.

Since the z-score of z2 is 0, we look up the area to the left of 0 in the z-table, which is 0.5000. This represents the percentage of students who scored below 253.

To find the percentage of students who scored between 167 and 253, we subtract the percentage below 167 from the percentage below 253:

Percentage = 0.5000 - 0.0228 ≈ 0.4772

Therefore, approximately 47.72% of the students scored between 167 and 253 on the exam.

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a) Poles: 0, -2i, +2i; Zeros: +I, -i. b) Number of asymptotic branches: 2. c) Asymptotes: Re(s) = -1, Re(s) = -∞. d) Center point(s): No center point(s). e) Branch departure/arrival angles: 180°, 0°, 180°.


a) The poles of the transfer function L(s) = (s² + 1) / (s(s² + 4)) are obtained by setting the denominator equal to zero, resulting in poles at s = 0, s = -2i, and s = +2i. The zeros are obtained by setting the numerator equal to zero, resulting in zeros at s = +I and s = -i.
b) The number of asymptotic branches is determined by the difference between the number of poles and zeros, which is 2 in this case.
c) The asymptotes can be found using the formula Re(s) = (2k + 1)π / n, where k ranges from 0 to (n-1), and n is the number of asymptotes. In this case, there are two asymptotes with Re(s) = -1 and Re(s) = -∞.
d) There are no center point(s) since the transfer function has no finite zeros or poles.
e) The branch departure/arrival angles can be calculated using the formula ∠G(s) = (2k + 1)180° / n, where k ranges from 0 to (n-1), and n is the number of asymptotes. In this case, the branch departure/arrival angles are 180°, 0°, and 180°, corresponding to the two poles and one zero.

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Scenario 1A:

Coinsurance amount is $90

Medicare payment is $360

Provider write-off is $290

Scenario 1B:

Remaining amount for Insurance and patient to pay is $350

Coinsurance amount is $70

Total paid by patient is $170

Medicare payment is $280

Provider write-off is $370

Scenario 1A:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Coinsurance amount (20% paid by patient): $

Medicare payment (80% of the PFS): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Coinsurance amount (20% paid by patient):

Coinsurance amount = 20% of the Medicare participating physician fee schedule (PFS)

Coinsurance amount = 0.2 * $450 = $90

Medicare payment (80% of the PFS):

Medicare payment = 80% of the Medicare participating physician fee schedule (PFS)

Medicare payment = 0.8 * $450 = $360

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $360 = $290

Scenario 1B:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Patient pays $100 remaining on their deductible

Remaining amount for Insurance and patient to pay: $

Coinsurance amount (20% of remaining amount): $

Total paid by patient (deductible & 20% of remaining): $

Medicare payment (80% of the remaining amount): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Remaining amount for Insurance and patient to pay:

Remaining amount for Insurance and patient to pay = PFS - remaining deductible

Remaining amount for Insurance and patient to pay = $450 - $100 = $350

Coinsurance amount (20% of remaining amount):

Coinsurance amount = 20% of the remaining amount

Coinsurance amount = 0.2 * $350 = $70

Total paid by patient (deductible & 20% of remaining):

Total paid by patient = remaining deductible + coinsurance amount

Total paid by patient = $100 + $70 = $170

Medicare payment (80% of the remaining amount):

Medicare payment = 80% of the remaining amount

Medicare payment = 0.8 * $350 = $280

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $280 = $370

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Answer:

-100 + x = 40

Step-by-step explanation:

According to the question:

Tyler's original height = -100 feet

Tyler's final height = 40

X to represent change in elevation

As initial + change = final, the equation would be:  

-100 + x = 40  

Please mark it as brainliest if it helps you!

I wasn't sure about my answer, so used the gauthmath app.

The artwork described seems to exhibit all of the following characteristics EXCEPT B. a dependence on Classical prototypes.

This suggests that the artist's style is more focused on individual expression (A), with a unique approach to their subject matter, rather than relying on traditional styles or motifs from the Classical period.

Additionally, the artwork demonstrates a limited use of shading and volume (C), which might indicate a more simplified or stylized approach to form and depth. This characteristic might be a deliberate choice by the artist to emphasize certain elements or create a specific visual effect.

Furthermore, the strong linear sense (D) present in the work implies that the artist has prioritized clean, well-defined lines to establish the shapes and contours of the subjects. This approach can contribute to the overall clarity and structure of the composition.

To sum up, the artwork in question seems to prioritize individual expression, simplified shading and volume, and a strong linear sense, while not depending heavily on Classical prototypes for its inspiration.

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A. By the given conditions, the function f has a root in the interval [a, b].

B. The given conditions provide information about the function f and its derivatives.

Let's analyze the conditions step by step:

1. f(a) < 0 and f(b) > 0: This implies that function f takes negative values at the left endpoint a and positive values at the right endpoint b.

In other words, the function changes the sign between a and b.

2. f'(x) > 0 for all x in (a, b): This condition states that the derivative of f, denoted as f'(x), is always positive in the open interval (a, b).

This indicates that the function is increasing within this interval.

3. f''(x) > 0 for all x in (a, b): This condition states that the second derivative of f, denoted as f''(x), is always positive in the open interval (a, b).

This indicates that the function is concave up within this interval.

By combining these conditions, we can conclude that the function f is continuous, increasing, and concave up within the interval (a, b).

Since f(a) < 0 and f(b) > 0, and the function changes sign between a and b, by the Intermediate Value Theorem, there exists at least one root of the function f in the interval [a, b].

Therefore, the main answer is that the function f has a root in the interval [a, b].

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Answer:
You will need 80 square feet of tile to cover the kitchen floor, leaving out the area used by the stove and refrigerator.

Step-by-step explanation:

Step 1: Calculate the area of the kitchen floor: 7' x 16' = 112 square feet.

Step 2: Calculate the area of the stove: 3' x 4' = 12 square feet.

Step 3: Calculate the area of the refrigerator: 4' x 5' = 20 square feet.

Step 4: Subtract the areas of the stove and refrigerator from the total area of the kitchen floor: 112 - 12 - 20 = 80 square feet.

Answer:

y = -1/3x - 7/3

Step-by-step explanation:

To find the slope, you have to plug the values into the slope formula.

y2 - y1/ x2 - x1

-4 - (-2) / 5 - (-1)

-1/3

Now to find the y-intercept, plug in one of the coordinates into the equation.

y = -1/3x + b

-2 = -1/3(-1) +b

-2 = 1/3 + b

-7/3 = b

The equation is y = -1/3x - 7/3.  

The Solution is Y = - ( 1 / 3 )X - 7 / 3 where points are ( 5 , - 4) and ( - 1 , - 2) that passes through a straight line. Y = MX + C is the Formula for Straight line equation.

As per given problem, M is Slope

M = (Y2 - Y1) / (X2 - X1)

M = (- 4 - (- 2)) / ( 5 - (- 1))

M = - (1 / 3)

Now, Line becomes

- 2 = - ( 1 / 3) x (- 1)+ C

- 2 = 1 / 3 + C

C = - (7 / 3)

So, Solution:  Y = - (1 / 3)X - (7 / 3)

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Answer:

C. y = -1/2x + 32

Step-by-step explanation:

I just took the test :)

Answer:

y=-1/2x+32

Step-by-step explanation:

The sum of the exterior angles of a decagon is 360 degree if each exterior angle measure is 36 degree.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

We have:

Decagon, in which the number of sides is 10

The formula for the sum of the interior angles in n number of polygon:

Sum = 180(n - 2)

Plug n = 10

Sum = 180(10-2)

Sum = 1440

Each interior angle = 1440/10 = 144 degree

Each exterior angle = 180 – 144 = 36 degree

The sum of the exterior angles = 36×10 = 360 degree

Similarly, we can find any angle measure for interior or exterior by using the formula:

Sum = 180(n—2)

Where n is the number of sides.

Thus, the sum of the exterior angles of a decagon is 360 degree if each exterior angle measure is 36 degree.

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If Ethan watches fewer than 6 movies per month, Plan A would be more expensive. If he watches more than 6 movies per month, Plan B would be more expensive.

For Plan A, the monthly cost is composed of a fixed fee of $28 plus a variable fee of $2.50 per movie watched. So, if Ethan watches x movies per month, the monthly cost for Plan A can be represented by the equation:

A = 28 + 2.5x

Here, A represents the monthly cost of Plan A, and x represents the number of movies Ethan watches per month.

For Plan B, the monthly cost is also composed of a fixed fee of $37, but the variable fee per movie watched is only $1. So, if Ethan watches x movies per month, the monthly cost for Plan B can be represented by the equation:

B = 37 + 1x

Again, B represents the monthly cost of Plan B, and x represents the number of movies Ethan watches per month.

To find the number of monthly movies watched, x, that would make the two plans have an equal monthly cost, we need to solve the equation:

A = B

So, we can substitute the equations for A and B to get:

28 + 2.5x = 37 + 1x

Now we can solve for x:

2.5x - 1x = 37 - 28

1.5x = 9

x = 6

So, if Ethan watches 6 movies per month, the monthly cost of Plan A and Plan B would be equal, at $41 per month.

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Answer:

x = 17

Step-by-step explanation:

The angles are same side interior angles and they will add to 180 when the lines are parallel

6x+8  + 4x+2 = 180

10x+10 = 180

Subtract 10 from each side

10x+10-10 =180-10

10x = 170

Divide by 10

10x/10 = 170/10

x = 17

Answer:

x = 17

Step-by-step explanation:

Theorem:

If two lines are cut by a transversal such that same-side interior angles are supplementary, then the lines are parallel.

For the lines to be parallel, the sum of 6x + 8 and 4x + 2 must equal 180.

6x + 8 + 4x + 2 = 180

10x + 10 = 180

10x = 170

x = 17