Convert the following angle from degrees to radians. Express your answer in simplest form.

195°

Therefore, the absolute minimum value of f on the interval [-1, 6] is -1, and the absolute maximum value is 15625.

To find the absolute minimum and absolute maximum values of the function f(x) = (x^2 - 1)^3 on the interval [-1, 6], we need to evaluate the function at its critical points and endpoints.

First, let's find the critical points by taking the derivative of f(x) and setting it equal to zero:

f(x) = (x^2 - 1)^3

f'(x) = 3(x^2 - 1)^2 * 2x

Setting f'(x) = 0, we have:

3(x^2 - 1)^2 * 2x = 0

This equation is satisfied when x = -1, 0, and 1.

Next, we evaluate f(x) at the critical points and endpoints:

f(-1) = (-1^2 - 1)^3 = 0

f(0) = (0^2 - 1)^3 = -1

f(1) = (1^2 - 1)^3 = 0

f(6) = (6^2 - 1)^3 = 25^3 = 15625

Now we compare the function values to determine the absolute minimum and absolute maximum:

The function has an absolute minimum value of -1 at x = 0.

The function has an absolute maximum value of 15625 at x = 6.

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It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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Answer:

normal force decreases

Step-by-step explanation:

N=mgcosθ, and cosine decreases as theta increases

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Answer:

A) decreases

Step-by-step explanation:

As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.

a) The expected number of calls in one hour is 60.

b) The probability of three calls in a five-minute period is approximately 0.1404.

c) The probability of no calls in a five-minute period is approximately 0.0067.

a. The expected number of calls in one hour can be calculated by multiplying the rate of calls per minute by the number of minutes in an hour:

Expected number of calls in one hour = 1 call/minute x 60 minutes/hour = 60 calls/hour

Therefore, the expected number of calls in one hour is 60.

b. The number of calls in a five-minute period follows a Poisson distribution with a mean of λ = (1 call/minute) x (5 minutes) = 5. The probability of three calls in a five-minute period can be calculated using the Poisson probability formula:

P(X = 3) = (e^(-λ) * λ^3) / 3!

where X is the number of calls in a five-minute period.

P(X = 3) = (e^(-5) * 5^3) / 3! = 0.1404 (rounded to 4 decimals)

Therefore, the probability of three calls in a five-minute period is approximately 0.1404.

c. The probability of no calls in a five-minute period can also be calculated using the Poisson probability formula with λ = 5:

P(X = 0) = (e^(-λ) * λ^0) / 0! = e^(-5) = 0.0067 (rounded to 4 decimals)

Therefore, the probability of no calls in a five-minute period is approximately 0.0067.

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To design an economical wall footing, determine the loads, calculate the dimensions, check the bearing capacity of the soil, design the reinforcement based on material properties, and draw a final design incorporating all necessary details.

1. Determine the loads:
The dead load of the wall is given as 291.88 kN/m, and the live load is 218.91 kN/m.

2. Calculate the total load:
To calculate the total load, add the dead load and live load together:
Total load = Dead load + Live load

3. Determine the dimensions of the footing:
The width of the wall is given as 300 mm. We need to convert this to meters for consistency:
Width of the wall = 300 mm = 0.3 m

4. Calculate the area of the footing:
To determine the area of the footing, divide the total load by the allowable soil pressure (qa):
Area of the footing = Total load / qa

5. Determine the depth of the footing:
The bottom of the footing is stated to be 1.22 m below the final grade.

6. Calculate the volume of the footing:
To calculate the volume of the footing, multiply the area of the footing by the depth of the footing:
Volume of the footing = Area of the footing x Depth of the footing

7. Determine the weight of the soil:
The weight of the soil is given as 15.71 kN/m³.

8. Calculate the weight of the soil on the footing:
To calculate the weight of the soil on the footing, multiply the volume of the footing by the weight of the soil:
Weight of the soil on the footing = Volume of the footing x Weight of the soil

9. Calculate the total load on the footing:
To determine the total load on the footing, add the weight of the soil on the footing to the total load:
Total load on the footing = Total load + Weight of the soil on the footing

10. Determine the allowable bearing capacity of the soil:
The allowable soil pressure (qa) is given as 191.52 kPa.

11. Check the allowable bearing capacity of the soil:
Compare the total load on the footing to the allowable bearing capacity of the soil. If the total load is less than or equal to the allowable bearing capacity, the design is acceptable. Otherwise, adjustments need to be made.

12. Design the reinforcement:
Given that fy = 413.7 MPa and fc = 20.7 MPa, we can design the reinforcement for the wall based on these values. The specific design will depend on the structural requirements and engineering standards in your area.

13. Draw the final design:
Based on the calculated dimensions, load, and reinforcement requirements, you can create a detailed drawing of the final design, including the dimensions of the footing, reinforcement details, and any other necessary information.

Remember, the design must be economical, so it's important to consider material costs and construction efficiency while ensuring the structure meets the necessary safety standards and requirements.

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The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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Answer:

   - A bag of rice is $16.9

   - A bag of flour is $5.20

Step-by-step explanation:

Let R and F stand for the price of a bag of Rice and Flour, respectively.

We can use the information provided to set an equation that will predict the total cost for that restaurant, given the quantities of rice and flour received (Restaurants A and B)

A) 4R + 2F = 78   [4 bags of rice and 2 bags of flour, when multiplied by the prices per bag, R and F, will result in a total cost of $78.

B)  3R + 4F = 71.5  [Now it is 3 bags of rice and 4 of flour, for a total cost of $71.50

We have 2 equations and 2 unknowns.  We can use substitution to find the answers.  Take one of the equations and reorganize it to isolate one of the variables (R or F).  We'll take the equation for A and isolate F

---

A) 4R + 2F = 78

     2F = 78-4R      [subtract 4R from both sides]

       F = 39-2R      [divide both sides by 2]

We've isolated F, and we can use this definition of F in the second equation:

===

B)  3R + 4F = 71.5

3R + 4(39 - 2R) = 71.5  [Use the definition of F derived above.  In this manner, we have legally eliminated one of the two variables.  (Sneaky, effective, and fun)]

3R + 156 - 8R = 71.5   [Multiply, combine like terms, and simplify]

-5R = -84.5                  [Isolate R]

R = $16.9                      A bag of rice costs $16.9

Now use the price of rice (R=$16.9) in one of the equations.  Since the rearranged equation we used above is already conveniently written for F, we'll use it:

F = 39 - 2R

F = 39 - 2(16.9)

F = 39 - 33.8

F = $5.20                     A bag of flour costs $5.20

===

CHECK:

Do these two prices satisfy both equations we first formulated?

Restaurant A:  4R + 2F = 78?

                        4(16.9) + 2(5.20) = 78  YES

Restaurant B:  3R + 4F = 71.5?

                        3(16.9) + 4(5.20) = 71.5  YES

These are the correct answers.

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following inequality

solvinfg for w:

It takes Steve 12 hours to process the research paper alone.

Let's use the terms "research," "hours," and "paper" in our answer.

Step 1: Represent the rate of work for Alan and Steve using variables.
Let A = Alan's rate of work (paper per hour) and S = Steve's rate of work (paper per hour).

Step 2: Set up equations based on the given information.
Alan can complete the research paper in 6 hours, so his rate is 1/6 paper per hour: A = 1/6.
Together, Alan and Steve can complete the paper in 4 hours, so their combined rate is 1/4 paper per hour: A + S = 1/4.

Step 3: Substitute the known value of A (Alan's rate) into the equation and solve for S (Steve's rate).
(1/6) + S = 1/4

Step 4: Solve for S.
To do this, first find a common denominator for the fractions, which is 12. Then, rewrite the equation with equivalent fractions:
(2/12) + S = (3/12)

Now, subtract 2/12 from both sides of the equation:
S = (3/12) - (2/12)

This simplifies to:
S = 1/12

Step 5: Determine how long it takes Steve to complete the research paper alone.
Since Steve's rate is 1/12 paper per hour, it takes him 12 hours to complete the research paper alone.

Answer: It takes Steve 12 hours to process the research paper alone.

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Answer: 12 ft

Step-by-step explanation:

Our equation is y = 15.2 - .537x where "y" is the temperature and "x" is the depth. We want to find the depth when the temperature is 9 degrees. Therefore, we need to plug in y = 9 and find x:

9 = 15.2 - .537x

We subtract 15.2 from both sides and divide by -1 on both sides so that we are working with positive numbers only:

6.2 = .537x

We then divide both sides by .537 to isolate x:

11.55 = x

This rounds to 12, meaning that at 9 degrees, the depth is 12ft.

The number that can be used to complete the area model is 210 and it can be used with numbers that are dragged are 100,100,10 bearing in mind that numbers may be used more than once

We already know that we have 14 colored tiles and that each of the area models is represented by 15 colored kits

The number of colored tiles in 15 kits is 210.

To find the total number of kits to use to complete the area model, you can multiply the number of tiles per kit (14) by the number of kits (15):

14 x 15 = 210

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Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The denominator of the fraction is 20.

Assume the fraction’s denominator is represented by “x”. The numerator is 5 less than the denominator, based on the information provided. This may be written as (x – 5). And we are told that the fraction is equal to 3/4. As a result, we may write the equation as

⇒(x – 5) / x = 3/4

To remove the fraction, cross-multiply the equation. Multiply the denominator of the left fraction by the numerator of the right fraction and vice versa:

⇒4(x – 5) = 3x

⇒4x – 20 = 3x

⇒4x – 3x = 20

⇒x = 20

Therefore, the denominator of the fraction is 20.

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The correct question is-

The numerator of a certain fraction is 5 less than the denominator if the fraction is equal to 3/4 what is the denominator of this fraction?

Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

The area of the triangle JHI is 8.75 square units.

From the given figure,

Area of a ΔJHI = Area of a rectangle - (Area of 3 triangles)

= 5×4 - (1/2 ×3×4 + 1/2 ×2×3 + 1/2 ×1×5)

= 20 - (6+3+2.5)

= 20 - 11.25

= 8.75 square units

Therefore, the area of the triangle JHI is 8.75 square units.

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Answer:

10^8 pennies in a million dollars.

Step-by-step explanation:

I will work with the accepted number of pennies in a dollar:  100.

Then the number of pennies in a million dollars is

p = 100*10^6, or 1*10^8,  or just 10^8.

Answer:

9. The 5 bags for $25 is a better deal

10. You would need $16.72

Step-by-step explanation:

9. Divide 25/5=5 and 42/7=6

The 5 bags for $25 is a better deal because it's the smallest answer.

10. Divide $12.54/6=$2.09 per book

Multiply $2.09*8=$16.72 for 8 books

Answer:

9. The 5 bags for $25.00 is the best offer.

10. 8 books is $16.72.

Step-by-step explanation:

9. Because you have to find out how much each bag costs so you divide the total cost by the ammount of bags. When you do this you get $5 dollars a bag for the 5 bags and $6 dollars a bag for the 7 bags.

10. You need to find out how much each book cost so you divide the amount of money by 6 and you get $2.09. Then you multiple 8 by 2.09 and you get 1672 but then you have to move the decimal to the left two times and you end up with $16.72.

Answer:

i dont know

Step-by-step explanation:

But i think it is 10/1 20/2 and 60/6

I dont do slopes in Math but by the power of observation I beileve I have figured it out    

Answer:

1/10 2/20

Step-by-step explanation:

Those are the answers hope this helped.

Answer:

6

Step-by-step explanation:

y=2x+4

y=2(1)+4

y=2+4

y=6

Congruent quadrilateral related parts are congruent.

The true statements are:

Statements 2, 4, and 6 are Not Congruent

Statements 1, 3, and 5 are Congruent

From the given figure:

Quadrilaterals 1, 2 and 4 are congruent

Quadrilateral 3 is not congruent to any of the other quadrilaterals.

The true statements are:

Quadrilateral 1 and quadrilateral 2 Congruent

Quadrilateral 1 and quadrilateral 3 Not Congruent

Quadrilateral 1 and quadrilateral 4 Congruent

Quadrilateral 2 and quadrilateral 3 Not Congruent

Quadrilateral 2 and quadrilateral 4 Congruent

Quadrilateral 3 and quadrilateral 4 Not Congruent

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the dimensions of the dumpster that will minimize its surface area

length l = 6.32

width w =  1.58

height h = 0.39

Length = l

width = w

height = h

given that length is four times its width

l = 4w

Now, the formula for the surface area of a cube is;

S = 2lh + 2lw + 2wh

substitute l = 4w in the above equation

S = 2(4w)h+2(4w)w+2wh

S = 8wh+8\(w^{2}\)+2wh

S = 10wh + 8\(w^{2}\)

formula for the volume of a cube is;

V = lwh

now substitute l=4w in the above equation

V = (4w)wh

V = 4\(w^{2}\)h

h = 4\(w^{2}\)/V

Put V/2w² for h in the surface area equation to get;

S= 8w² + 10w(V/4w²)

 = 8w² + 5V/2w

given that volume V = 25.6 substitute that in the above equation

S = 8w² + 5(25.6)/2w

  = 8w² + 128/2w

Since we want to minimize the surface area, let us find the first derivative of S to get;

S' = 16w - 128/2w²

At S' = 0

0 = 16w-  128/2w²

16w =  128/2w²

32w³ = 128

w³ = 128/32

w³ = 4

w = \(\sqrt[3]{4}\)

w = 1.58 yds

since l = 4w substitute the value of w in that

l = 4(1.58) = 6.32

h = 4\(w^{2}\)/V = 4(\(1.58^{2}\))/25.6

h = 0.39

the dimensions are

length l = 6.32

width w =  1.58

height h = 0.39

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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Answer:

Step-by-step explanation:

2

The total area under a probability density function is always equal to 1.

This means that the probability of any possible outcome occurring in the given probability distribution is 1, or 100%. The area under the probability density function represents the likelihood of a random variable falling within a particular range of values, and the total area represents the probability of all possible outcomes.

The probability density function can be used to calculate the probability of a random variable taking on a specific value, as well as the probability of a random variable falling within a certain range of values. The area under the probability density function can be calculated using integration techniques.

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The solution y = -1/(t^2 + 2t + 3) is defined for all real values of t, and the largest interval in which the solution is defined is (-∞, ∞).

To solve the initial value problem dy/dt = 2(t + 1)y^2, y(0) = -1/3, we can separate the variables and integrate both sides with respect to t.

Starting with the given differential equation:

dy/y^2 = 2(t + 1) dt

Integrating both sides:

∫(dy/y^2) = ∫(2(t + 1) dt)

Integrating the left side using the power rule for integration gives:

-1/y = t^2 + 2t + C1

To find the constant of integration, we use the initial condition y(0) = -1/3:

-1/(-1/3) = 0^2 + 2(0) + C1

3 = C1

Therefore, the equation becomes:

-1/y = t^2 + 2t + 3

Next, we can solve for y:

y = -1/(t^2 + 2t + 3)

Now, let's determine the largest interval in which the solution is defined. The denominator of y is t^2 + 2t + 3, which represents a quadratic polynomial. To find the interval where the denominator is non-zero, we need to consider the discriminant of the quadratic equation.

The discriminant, Δ, is given by Δ = b^2 - 4ac, where a = 1, b = 2, and c = 3. Substituting the values, we have:

Δ = (2)^2 - 4(1)(3) = 4 - 12 = -8

Since the discriminant is negative, Δ < 0, the quadratic equation t^2 + 2t + 3 = 0 has no real solutions. Therefore, the denominator t^2 + 2t + 3 is always positive and non-zero.

Hence, the solution y = -1/(t^2 + 2t + 3) is defined for all real values of t, and the largest interval in which the solution is defined is (-∞, ∞).

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Answer:

y = (3/2)x + 2

Step-by-step explanation:

The slope-intercept form of the equation of a line is:

y = mx + b

m = slope, and (x, y) can be substituted by the coordinates of the given point.

8 = (3/2)(4) + b

8 = 6 + b

b = 2

y = (3/2)x + 2

The statement that best describes the infοrmatiοn presented in the chart is: "The number οf hurricanes was increasing but has decreased in recent years."

Hurricanes, knοwn generically as trοpical cyclοnes, are lοw-pressure systems with οrganized thunderstοrm activity that fοrm οver trοpical οr subtrοpical waters. They gain their energy frοm warm οcean waters.

The chart shοws the number οf hurricanes οf categοry 1 οr higher that οccurred during specific series οf years, and it indicates that the number οf hurricanes increased frοm 13 in 1980-1989 tο 23 in 2000-2009, and then decreased tο 10 in 2010-2017.

Therefοre, the chart suggests that the number οf hurricanes was increasing, but it has decreased in recent years. The chart dοes nοt prοvide any infοrmatiοn abοut tοrnadοes in Finleyville οr the relatiοnship between the number οf hurricanes and temperature.

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The statement that best describes the information in the graph is: "The number of hurricanes has increased but decreased in recent years." The graph shows that the number of Category 1 or greater hurricanes increased from 1980 to 2009, but decreased from 2010 to 2017.

Answer:

Squares have to have the same shape and size to be congruent. Therefore, not all squares are congruent, since not all of them are the same size. … This means that they have the same shape, although not necessarily the same size.

hope this helps

mark me brainliest

Step-by-step explanation:

Answer:

I have reason to believe its a

Step-by-step explanation:

Easy 9nth grade math :)