A student drives home from college on break. She travels 412 miles in 8 hours. What was the student’s speed in mph? Round to 1 decimal place. If the student wants to return to school in 6 hours, what should her average speed be? Round to 1 decimal place. Her father tells her not to travel back at over 60 mph. If 60 mph is her average speed, how long will it take her to get back to school? Round to 1 decimal place.

The coefficient of the second derivative (t2) is constant, so the equation is linear.

1. (1+y2)(d2y/dt2)+t(dy/dt)+y=et2  ->  2nd. order non-linear differential equation

2. t2(d2y/dt2)+t(dy/dt)+2y=sin t  ->  2nd. order linear differential equation

3. (d3y/dt3)+t(dy/dt)+(cos2(t))y=t3  ->  3rd. order non-linear differential equation

4. y''-y+y2=0  ->  2nd. order non-linear differential equation

The order of a differential equation is the highest derivative involved in the equation. For example, in the equation 1 + y2(d2y/dt2) + t(dy/dt) + y = et2, the highest derivative is the second derivative (d2y/dt2), so this equation is of 2nd order. Linearity is determined by whether the coefficients of each derivative are constants, or whether they depend on the function y and its derivatives. In this equation, the coefficient of the second derivative (1+y2) is not constant, so the equation is non-linear. Similarly, in equation t2(d2y/dt2)+t(dy/dt)+2y=sin t, the coefficient of the second derivative (t2) is constant, so the equation is linear.

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Equation that represents the Marks and study hours of Adams is y = 7.5x + 60.

A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given a linear regression graph that has a linear equation.

Slope intercept form of a line

y = mx + c

where,

m is the slope

c is the y-intercept(Where x is zero)

In our case,

y-intercept = 60

Thus, the equation of line will be:

y = mx + 60

Coordinates of the line are given (4, 90). So, these points will Satisfy the equation.

90 = 4*m + 60

4.m = 30

m = 7.5

Thus, equation of the line will be:

y = 7.5x + 60

Adam's test score after studying for 6 hours:

y = 7.5 * 6 + 60

y = 45 + 60

y = 105

therefore, Equation that represents the Marks and study hours of Adams is y = 7.5x + 60.

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The graph for the given mode function, y ≥ |x| - 4 is attached below.

In mathematics, the modulus function is a function for which any input value of x, output will be always positive

Given that,

The modulus function,

y  ≥  |x| - 4

We can write given function in a following two ways-

y  ≥  x - 4

y  ≥  -x - 4

So, for any value of x

y should be greater than modulus functions value

Plotting graph for  y  ≥  x - 4

So first draw line  x - 4

Now, here we have inequality sign

So left side region will be our desired space

Similarly, Plotting graph for  y  ≥  -x - 4

So first draw line  -x - 4

Now, here we have inequality sign

So right side region will be our desired space

Hence, Graph is drawn for the given function

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Answer:

Why don't you use this app and take a picture and see if someone got the answer

The vertex angle of the isosceles triangle is 22°.

What is isosceles triangle?

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.

We know that an isosceles triangle is composed of a vertex angle and two base angles. The base angles are congruent to each other. We also know that the sum of a triangle's angles is 180degrees.

Base angle = 3vertex angle+13.

=> 2base angle + vertex angle = 180°

=> 2(3 vertex angle +13)+vertex angle = 180°

=> 6 vertex angle+26+vertex angle = 180

=> 7 vertex angle = 180-26

=> 7 vertex angle = 154

=> vertex angle = 154/7 = 22°.

Hence the vertex angle of the isosceles triangle is 22°.

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Step-by-step explanation:

after mixing 1 can of concentrate and 3 cans of water, we will have 4 cans of juice.

the volume of 1 can is (as for any cylinder or regular 3D object)

base area × height

for a cylinder the bar area is the area of a circle

pi×r²

r is the radius, which is half of the diameter.

in the picture it is not fully clear what is 2.25 in long : the diameter of the radius ?

I suspect it is the diameter.

so, the radius of our cans is 2.25/2 = 1.125 in

the volume of 1 can is

pi×1.125²×4.25

and the volume of all 4 cans of juice is then

4×pi×1.125²×4.25 = 17×3.14×1.265625 = 67.5590625 in³

≈ 68 in³

so, your answer is 68.

Answer:

30

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

Use  Pythagorean theorem a^2 + b^2 = c^2:

18^2 + 24^2 = c^2

324 + 576 = c^2

900 = c^2

c = 30

Answer: 20 different total voting combination

Step-by-step explanation: So we have 5 bands. Lets called them A, B, C, D, and E.

If John has to vote on his favorite and second favorite that means we will be selecting 2 bands out of the 5 possible to choose from.

To find the TOTAL amount of different combinations we need to pair up bands and find all the combo's.

Here are the results/totals:

AB

AC

AD

AE

BA

BC

BD

BE

CA

CB

CD

CE

DA

DB

DC

DE

EA

EB

EC

ED

So this is 20 different total voting combinations.

If you want to do it simpler without listing you can take the the 5 bands and multiple by 4 since you know each initial band (A, B, C, D, and E) will be paired with another band other than itself.

Using Algebraic Expressions, The ratio of any two numbers is five: 5/x

Many students find algebra intimidating since it's the first math course they take where they have to deal with variables, abstract ideas, and problem-solving skills. Additionally, not enough is frequently done in the classroom to relate algebra to students' daily lives and explain why it is important to comprehend.

We take into consideration a number "x" for the algebraic expression.

Two numbers are divided to produce the quotient. The ratio between five units and any number "x" is what we have here.

a mathematical expression

Quantile = 5/x

We will get various quotient outcomes depending on the value we provide to the variable "x."

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Full question"

The ratio of 5 between any number.

The functions are 0, -2 and 1 for the mentioned function is 4, - 16 and 2.

Firstly we will represent the function in equation form. Then we will calculate the result by keeping each value of function.

f(x) = x³ - 3x² + 4

Calculating result when function is 0

f(x) = 0³ - 3×0² + 4

f(x) = 0 - 0 + 4

f(x) = 4

Calculating result when function is -2

f(x) = (-2)³ - 3×(-2)² + 4

Finding square and cube

f(x) = -8 - 3×4 + 4

Performing multiplication

f(x) = - 8 - 12 + 4

Performing addition

f(x) = - 20 + 4

Performing subtraction

f(x) = - 16

Calculating result when function is 1

f(x) = 1³ - 3×1² + 4

f(x) = 1 - 3 + 4

Performing addition

f(x) = 5 - 3

Performing subtraction

f(x) = 2

Thus, functions are 4, -16 and 2.

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Answer:

42 divided by 6=7 so in each vase there are 7 flowers

Step-by-step explanation:

The peak of the mountain has a height of 14805 feet.

In this problem we find the case of an exponential function for atmospheric pressure (p), in pounds per square inch, in terms of height (x), in miles, whose expression is introduced below:

[tex]p(x) = 14.7 \cdot e^{- 0.21\cdot x}[/tex], for x ≥ 0.

If we know that p(x) = 8.164 lb / in², then the height of the peak of a mountain is:

[tex]8.164 = 14.7\cdot e^{-0.21 \cdot x}[/tex]

[tex]0.555 = e^{-0.21\cdot x}[/tex]

Then, by relationship between exponential and logarithmic functions and logarithm properties:

㏑ 0.555 = - 0.21 · x · ㏑ 1

㏑ 0.555 = - 0.21 · x

x = - (1 / 0.21) · ㏑ 0.555

x ≈ 2.804

Finally, convert miles into feet:

x = 2.804 mi × (5,280 ft / 1 mi)

x = 14805.12 ft

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The heights and locations of the three peaks in this activity are: Peak 1 is 4,064 meters (13,320 feet) and located in Ladakh, India; Peak 2 is 8,848 meters (29,029 feet) and located in Nepal; and Peak 3 is 8,611 meters (28,251 feet) and located in Pakistan.

Peak 1: Height: 4,064 m (13,320 ft), Location: Ladakh, India

Peak 2: Height: 8,848 m (29,029 ft), Location: Nepal

Peak 3: Height: 8,611 m (28,251 ft), Location: Pakistan

Peak 1: Height: 4,064 m (13,320 ft), Location: Ladakh, India

This means that the height of Peak 1 is 4,064 meters (13,320 feet) and it is located in Ladakh, India.

Peak 2: Height: 8,848 m (29,029 ft), Location: Nepal

This means that the height of Peak 2 is 8,848 meters (29,029 feet) and it is located in Nepal.

Peak 3: Height: 8,611 m (28,251 ft), Location: Pakistan

This means that the height of Peak 3 is 8,611 meters (28,251 feet) and it is located in Pakistan.

The heights and locations of the three peaks in this activity are: Peak 1 is 4,064 meters (13,320 feet) and located in Ladakh, India; Peak 2 is 8,848 meters (29,029 feet) and located in Nepal; and Peak 3 is 8,611 meters (28,251 feet) and located in Pakistan.

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The standard deviation of random variable K is 15.49  (option D ) and this can be determined by using the formula of mean and standard deviation.

Given,

The mean of geometric distribution of random variable K = 16

Formulae for finding mean,

                                      mean = 1/p

Substitute the value of the mean in the above formula in order to determine the value of 'p'.

[tex]16 =\frac{1}{p}[/tex]

[tex]p = 0.0625[/tex]

The formulae for standard deviation :

   S.D.=[tex]\frac{\sqrt{1-p} }{p}[/tex]

Now substitute the value of p in the above equation,

S.D. [tex]= \frac{\sqrt{1-0.0625} }{0.0625}[/tex]

       [tex]= 15.49[/tex]

Hence, the answer is option D.

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The price per foot is $0.29

Given,

A 3-yard piece of cotton cloth costs =  $2.61

1 Yard = 3 Foot

so, 3 Yard = 9 Foot

The Cost of cotton cloth per foot,

= 2.61/9

= 0.29

Therefore, the price per foot is $0.29

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Option D is the correct answer that is The average rate of change of the volume with respect to the radius when the volume changes from 1 cubic inch to 3 cubic inches.

The average rate of change of the volume with respect to the radius when the volume changes from 1 cubic inch to 3 cubic inches is represented in v(3)-v(1)/3-1.

The difference in volumes is

V(r+3) - V(r) = 4π [tex](r+3)^{3}[/tex] /3 - 4π [tex]r^3}[/tex]/3

= 4π/3( (r+3)[tex]^{3}[/tex] -  [tex]r^{3}[/tex])

= 4π/3( [tex]r^{3}[/tex]+ 9[tex]r^{2}[/tex]+ 27r + 27 -  r∧3 )

= 4π/3(9 [tex]3^{3}[/tex] + 27r + 27 )

= 12π( [tex]r^{2}[/tex]+ 3r + 3 ) in cube

A balloon is a sphere shape. A sphere is a solid figure where each endpoint is equidistant from the center. It is like a 3-Dimensional version of a circle shape. The volume of a sphere is 4/3πr∧3 and its surface area is  4πr∧2. Here r is the radius of the sphere.

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Ten to fifty is the range of the scores. The most frequent result is a 10 with a right-skewing bias.

Probability histogram

The height of each bar must be equal to the probability, the width of each bar must be the same, and the bars must be centered on the amount of money gathered.

The distribution is skewed to the right because the highest bar in the histogram is to the left and there is a tail of lower bars to its right.

The most frequent score is 10 due to the fact that the top bar in the histogram is centered at 10.

The result is:

Ten to fifty is the range of the scores.

The most frequent result is a 10 with a right-skewing bias.

Ten to fifty is the range of the scores.

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The cable company with the best rate of price per channel is

Tel-EVision.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

TV Watchers—$30.80 for 70 channels.

The unit rate.

= 30.80/70

= 0.44

Tel-EVision—$46.40 for 145 channels.

The unit rate.

= 46.40/145

= 0.32

Channels Galore—$40.80 for 120 channels

The unit rate.

= 40.80/120

= 0.34

Thus,

Tel-EVision cable company has the best rate of price per channel.

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If there are no forgeries, then total weight will be

= (1+2+3+4+5+6+7+8+9+10) = 55 grams

given that

they have 10 bags full of coins

in each bag are infinite coins.

but one bag is full of forgeries, and you can't remember which bag.

you know that genuine coins weigh= 1 gram

forgeries weight = 1.1 gram

now, we need to find which bag has  forgeries  in minimum readings

then take 1 coin from the first bag, 2 coins from the second bag . . . 10 coins from the tenth bag

If there are no forgeries, then total weight will be

= (1+2+3+4+5+6+7+8+9+10) = 55 grams

Therefore total weight should be 55 grams if the total weight is more than 55 grams then it has forgeries coins

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Total weight=55gm ,then there is no forgeries coin bag

1 bag with forgeries = take 1 coin from first bag

from 2 bag = take 2 coin

and similarly with all 10 bags.....

from 10th bag = take 10 coin

if there is no forgeries ,then  total weight    = (1+2+3+4+5+6+7+8+9+10)

                                                                        =55gm

If bag weight 55.3 than we know that there are 3 forgeries.

So total weight=55 ,then there is no forgeries coin bag if weight is more than 55 than there is forgeries coin.

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The mean number of medals won by the United States during the first four summer Olympic Games is 86 medals.

1904: 78 medals

1908: 82 medals

1912: 88 medals

1920: 94 medals

Mean = 86 medals

1. Add the total number of medals awarded to the US during the first four summer Olympic Games: 78 + 82 + 88 + 94 = 342

2. Divide the total number of medals by the number of Olympic Games (4): 342 / 4 = 85.5

3. Round the mean to the nearest whole number: 86 medals

The mean number of medals won by the United States during the first four summer Olympic Games is 86 medals.

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The number of cycles per day and the production quantity per cycle.

Number of cycles per day = (Product Daily Quantity/Production Quantity per Cycle)

For Product A:

Number of cycles per day = (18/Production Quantity per Cycle)

For Product B:

Number of cycles per day = (16/Production Quantity per Cycle)

For Product C:

Number of cycles per day = (6/Production Quantity per Cycle)

For Product D:

Number of cycles per day = (14/Production Quantity per Cycle)

Using the data from the excel file, we can calculate the production quantity per cycle and the number of cycles per day.

For Product A:

Production Quantity per Cycle = 18/3.75 = 4.8

Number of cycles per day = 3.75

For Product B:

Production Quantity per Cycle = 16/2.5 = 6.4

Number of cycles per day = 2.5

For Product C:

Production Quantity per Cycle = 6/1.5 = 4

Number of cycles per day = 1.5

For Product D:

Production Quantity per Cycle = 14/2.25 = 6.2

Number of cycles per day = 2.25

Therefore, for this set of vehicles, the number of cycles per day and the production quantity per cycle are as follows:

Product A: 3.75 cycles per day, 4.8 units per cycle

Product B: 2.5 cycles per day, 6.4 units per cycle

Product C: 1.5 cycles per day, 4 units per cycle

Product D: 2.25 cycles per day, 6.2 units per cycle

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Step-by-step explanation:

reading the question thoroughly, we find out that volume (V) and radius (r) of the cone is given, and we just have to find out the length (h) of the cone

V = πr²h/3

Putting the given values in place,

V = 75.36 cm³

V = 75.36 cm³r = 2 cm

V = 75.36 cm³r = 2 cmπ = 3.14

Now, since we calculating for h, we can interpret the formula in the terms of h, i.e.

h = 3V/(πr²)

h = 3×75.36/(3.14×2²)

h = 226.08/12.56

h = 18 cm

Thus, the height of the ice cream cone is 18cm

Hope this helped!

Answer:

Width = 3.773 inches

Length = 79.227 inches-

Step-by-step explanation:

g = 7(3w)             Eq. 1

166 = 2(g+w)       Eq. 2

g = length

w = width

From Eq, 1:

g = 21w              Eq. 3

Replacing Eq. 3 in Eq. 2

166 = 2(21w + w)

166 = 2(22w)

166 = 44w

166/44 = w

w = 3.773

From Eq. 3

g = 21(3.773)

g = 79.227

Check:

From Eq. 2:

166 = 2(79.227 + 3.773) = 2 * 83

Answer: The equation that can be used to determine the total amount in Justin's account is:

b = 50 + (12 * w)

This equation represents the total amount in Justin's account, b, after w weeks. The equation starts with the initial amount, $50, which is the amount Justin had in his account before making any deposits. Then, it adds the amount deposited each week, $12, multiplied by the number of weeks, w. This results in the total amount in the account after w weeks.

In this equation the variable "w" represents the number of weeks that have passed and "b" represents the total balance.

Step-by-step explanation:

if Triangle ABC has sides that are 6 cm and 11 cm. The third is represented by the inequality 5 < 17.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that Triangle ABC has sides that are 6 cm and 11 cm

The third is represented by the inequality 5 < ×.

We know that the sum of sides of a triangle must be greater than the third side.

5<6+11

5<17

Hence, if Triangle ABC has sides that are 6 cm and 11 cm. The third is represented by the inequality 5 < 17.

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The values of p and q are given as follows:

p = 3.5, q = 6.

Hence the factored expression is given as follows:

2(x - 1.5)(x - 2)(x + 2).

The function f(x) is divisible by 2x² - 7x + 6, which has the roots given as follows:

x = 1.5 and x = 2.

(using a quadratic equation calculator with coefficients a = 2, b = -7 and c = 6).

Hence the following relation holds true, considering the linear factors of the function:

2x³ + px² + 8x + q = 2(x - 1.5)(x - 2)(x - a).

In which a is the third root.

Hence:

2x³ + px² - 8x + q = 2(x² - 3.5x + 3)(x - a)

2x³ + px² - 8x + q = 2(x³ - x²(3.5 + a) + x(3.5a + 3) - 3a)

2x³ + px² - 8x + q = 2x³ - x²(7.5 + 2a) + x(7a + 6) - 3a.

Hence the system of equations is given as follows:

From the second equation, the value of a is given as follows:

7a = -14

a = -2

Then the value of q is given as follows:

q = -3a = 6.

The value of p is given as follows:

p = 7.5 - 4

p = 3.5

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If the consumer buys both product X and product Y,  the consumer buy of each to maximize utility  will be 3X and 4Y.

Product X                         Product Y

Quantity   MUx  Quantity   MUy  

1                  32              1                    24

2                  28            2                    20

3                  24              3                     16

4                  20            4                       12

5                   16            5                      8

If the consumer can only buy product X, consumer buy and the total utility will be 5X and 120.

If the consumer buys both product X and product Y,  the consumer buy of each to maximize utility  will be 3X and 4Y.

When the consumer purchases the utility-maximizing

combination of product X and product Y, total utility will be 156.

A consumer is in equilibrium and is spending income in such a way that the marginal utility of product X is 40 units and Y is 16 units. The unit price of X is $5. The price of Y is: $2 per unit.

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The complete question is :

Based on the table below showing the marginal utility schedules for product X and product Y for a hypothetical consumer. The price of product X is $4 and the price of product Y is $2. The income of the consumer is $20. how much will the consumer buy of each in order to maximize utility?

Answer: The answer is: 525 millimeters of compound A are needed.

Step-by-step explanation:
You have to put it in equation form to solve for compound A. To do this use variables.

7(x) + 5(x) = 900
12(x) = 900
x = 900/12
x = 75
When we get 75 you have to plug it into compound A to get this:
7(75) = 525

To confirm our answer we plug in 75 to both variables.
7(75) + 5(75) = 900

I hope this was able to help you :D

Hello:

 --> this problem wants us to calculate the slope between (5, -6) and (2, 3)

So we are given two points:

  --> (x1, y1): (5, -6)

  --> (x2,y2): (2, 3)

Let's consider our formula needed:

 [tex]\text{Slope} = \dfrac{y2-y1}{x2-x1}=\dfrac{3--6}{2-5} =\dfrac{9}{-3} =-3[/tex]

Thus our slope is -3

Answer: -3

One kind of average is the mean. It is calculated by dividing the total number of values in a list of values, such as measurements or numbers, by the total number of values in the list.

Given data :

a ) Mean =

              x = [tex]\frac{\left \{ {{i=10} \atop {i=1}} \right.}{n} Xi[/tex] = 101 / 10 =  10.1 hundreds of dollars

The median is the 50th percentile To determine the location index for the median (2nd

quartile (p =50) we do the following:

The index is

                               i  = [tex]\frac{p}{100}[/tex] (n) = [tex]\frac{50}{100}[/tex] (10) = 5 integer

Since the index, 5, is an integer, the 2nd quartile is determined by finding the average of

the 5th and 6th values from the lower or higher end of the sorted data. This is:

                Median = [tex]Q_{2}[/tex] = [tex]\frac{10 + 11}{2}[/tex] = 10.5 hundreds of dollar

Mode = most frequently occurring observation = 11 hundreds of dollars ( two times )

Here i attached graph

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