Katherine drove home from college traveling an average speed of 65.1 mph and drove back to the college the following week at an average speed of 70.7 mph. If the total round trip took 7 hours, how much time did it take Katherine to drive from home back to college? Express the time in hours and minutes. Round to the nearest minute.

The dimensions of the rectangle are either 10cm x 24cm or

24cm x 10cm having perimeter 68 cm.

What is Pythagorean theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

A rectangle has 4 angles measure of each is 90°.

A diagonal of rectangle divides it into two right angled triangles.

Pythagorean theorem can be applied on these triangles to get the desired values.

According to the given question:  

Let the length and breadth of rectangle be  x  and  y .

Perimeter:  2x + 2y = 68 (Given)

Using Pythagorean theorem diagonal:  [tex]x^2+y^2=26^2[/tex]

Using perimeter,  x + y = 34

∴ x = 34 - y

Substituting this is the equation for diagonal

[tex](34-y)^2 +y^2=26^2\\1156 - 68y + 2y^2 = 676\\2y^2 - 68y + 480 = 0\\y^2 - 34y + 240 = 0\\(y - 10)(y - 24) = 0[/tex]

Therefore dimensions of rectangle are either 10cm x 24cm or

24cm x 10cm.

To know more about Pythagorean theorem visit

https://brainly.com/question/3346664

#SPJ1

The value of w in Angle  (w + 1)°  is 88

Given,

Angle (w + 1)°

Angle 91°

We have to find the value of w.

Here,

Linear pair of angles;

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.

Then,

Here the given angles are linear pair.

So,

(w + 1)° + 91 = 180

w + 1 + 91 = 180

w + 92 = 180

w = 180 - 92

w = 88

Then,

Angle (w + 1)° = 88 + 1 = 89°

Therefore,

The value of w in Angle  (w + 1)°  is 88

Learn more about linear pair of angles here;

https://brainly.com/question/17525542

#SPJ1

Answer:

[tex]f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)[/tex]

Step-by-step explanation:

The root -2 has a multiplicity of 2, and corresponds to a factor of [tex](x+2)^2[/tex].

The root 1 has a multiplicity of 1, and corresponds to a factor of [tex](x-1)[/tex].

The root 3 has a multiplicity of 1, and corresponds to a factor of [tex](x-3)[/tex].

So, [tex]f(x)=a(x+2)^2(x-1)(x-3)[/tex].

Since [tex]f(0)=10[/tex],

[tex]10=a(0+2)^2(0-1)(0-3) \\ \\ 10=12a \\ \\ a=\frac{5}{6} \\ \\ \therefore f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)[/tex]

After simplifying the equation, the chemist used 18 liters of 20% solution, 12 liters of 35% solution and 24 liters of 80% solution.

From the given question,

Let that chemist used x, y, z liters of 20%, 35% and 80% solution respectively.

Then according to the given information,

x+y+z=54..........(1)

As we know that in x liters having 20% acid, in y liters having 35% acid, in z liters having 80% acid and in total mixture having 50% acid.

So the equation should be

x ×20%+y×35%+z×80%=54×50%

On simplifying we get

20x+35y+80z=2700

4x+7y+16z=540...............(2)

As given that the number of 80% solution used in 2 times the number of liters of 35% solution used.

So z=2y

Now putting the value of z in equation (1)

x+y+2y=54

x+3y=54

Subtract 3y on both side

x+3y−3y=54−3y

x=54−3y

Now putting the value of x and z in equation (2)

4(54−3y)+7y+16×2y=540

Simplifying

216−12y+7y+32y=540

216+27y=540

Subtract 216 on both side

216+27y−216=540−216

27y=324

Divide by 27 on both side

27/27 y=324/27

y=12

Now putting the value of y in x=54−3y to find the value of x

x=54−3×12

x=54−36

x=18

Now putting the value of y in z=2y to find the value of z

z=2×12

z=24

Hence, the chemist used 18 liters of 20% solution, 12 liters of 35% solution and 24 liters of 80% solution.

To learn more about simplification of equation link is here

brainly.com/question/17350733

#SPJ1

Answer: x= -9

Step-by-step explanation:

Add like terms excluding x in: x+59+80+50=180

= x+189=180

[Transposing 189 to RHS]    x=180-189

So x= -9

Rewriting the expression |3r-15| without using absolute value bars gives

3r < 15 for r < 5

Absolute value do not give negative values it gives only the positive value

The given expression is |3r-15|

|3r - 15| < 0

|3r| < |-15|

3r < 15

If r < 5 then  say 4

|3r - 15|

|3 * 4 - 15|

|12 - 15|

|-3| = 3

Learn more about absolute values here:

https://brainly.com/question/729268

#SPJ1

The parabola has a minimum value of 5.75.

From the question, we have

f(x)=x^2-x+6

a=1, b=-1, c=6

Δ=b^2-4ac

=1-24

=-23<0

So f(x)=0 has no solution.

x=-b/2a=-(-1)/2=1/2

f(1/2)=1/4-1/2+6

=23/4  is the minimum

=5.75

The parabola has a minimum value of 5.75.

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

To learn more about multiplication visit: https://brainly.com/question/5992872

#SPJ9

Answer:

If you use y = mx + b, your equation would be y = -4x + 20

Step-by-step explanation:

M is always the slope, and to find the x-intercept, you just set y = 0 and in this case it would be 0 = -4x + 20. If you subtract 20 from both sides you get -20 = -4x and to find x, you just divide by -4 and get -20/-4, which equals 5. You're welcome :)

We need to determine the value of the y-intercept for this equation. Let's start by finding all other information about the x-intercept.

If the x-intercept is x = 5, f(5) = 0. So, now let's solve for b.

f(5) = -4(5) + b
0 = -4(5) + b
0 = -20 + b
0 + 20 = -20 + 20 + b
b = 20

We have m and b now, so:

y = -4x + 20

Answer:

The x-intercept is the point where the graph crosses the x-axis; it can be found by setting y = 0 and solving for x.

The y-intercept is the point where the graph crosses the y-axis; it can be found by setting x = 0 and solving for y.

1) g(x) = (x + 5)⁴

2) f(x) = 7 - x⁴

3) h(x) = ¼(x - 3)⁴

The graphs are labeled below.

The function will return the data type double.

Simply put, a function is a "chunk" of code that you can reuse repeatedly rather than having to write it out several times. Programmers can divide a problem into smaller, more manageable chunks, each of which can carry out a specific task, using functions.

Function declaration type will be as follows in general,

return type function name(argument 1, argument 2,...)

In the given question the declaration is double numbers (int x).

The return type is double, the name of the function is numbers and it has one argument which in an integer.

Hence, the return type of the function is double.

To learn more on function here:

brainly.com/question/5975436

#SPJ4

In triangle ABC, the value of angle A  is 60°.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the triangle ABC,

b=5cm, c=10cm

And by using Pythagoreans theorem,

a²=c²-b²

a²=10²-5²

a²=75

Use cosine rule to determine the angle A,

cosA=b²+c²-a²/2bc

cosA=25+100-75/2×5×10

cosA=50/100

cosA=1/2

cosA=cos60

⇒A=60°

To know more about Triangle on:

https://brainly.com/question/2773823

#SPJ1

Answer:

h(2) = 0

Step-by-step explanation:

1) 2 * 2 = 4

2) 4 * 3 = 12

3) 5 * 2 = 10
4) 12 - 10 - 2 = 0

Converting the given equations from standard form to slope intercept form gives

Information given in the question include

-2x+3y=-6

Standard form of linear equations is of the form Ax + By = C

The slope intercept form is y = mx + c

rearranging the equation

-2x + 3y = -6

3y = 2x - 6

y = 2x/3 - 2

The equation of the line in slope intercept form is y = 2x/3 - 2

Learn more about linear functions at:

https://brainly.com/question/29356636

#SPJ1

Answer:

3k(7k + 4)

Step-by-step explanation:

1. Find the GCF of all terms in the polynomial

2. Express each term as a product of the GCF and another factor.

3. Use distributive property to factor out GCF

The measure of the line segment AB is  36cm .

In the question ,

it is given that ,

The triangle ABC is a isosceles triangle ,

that means side AB = side BC ,

and the length of base AC = 24 cm .

given the perimeter of the triangle is 96 cm .

So ,

AB + BC + AC = 96

AB + AB + AC = 96       .....because AB = BC

2AB + AC = 96

Substituting the value of AC = 24 cm

2AB + 24 = 96

Subtracting 24 from both the sides , we get

2AB = 96 - 24

2AB = 72

Dividing both sides by 2 ,

we get ,

AB = 72/2 = 36 .

Therefore , The measure of the line segment AB is  36cm .

The given question is incomplete , the complete question is

Isosceles triangle ABC has a perimeter of 96 centimeters. The base of the triangle is Line segment A C and measures 24 centimeters.

What is the measure of Line segment AB ?

Learn more about Triangle here

https://brainly.com/question/13938498

#SPJ4

Poncho ha recorrido más trayecto de la carrera de bicicletas, con una fracción de 3/4 del recorrido.

Problema de comparación de fracciones:

Carmen lleva: 3/5 del trayecto

Memo: 4/7

Poncho: 3/4

Jocelyn: 1/2

Una forma de comparar las fracciones es usando un mismo denominador, esto es posible con el Mínimo Común Múltiplo (MCM):

MCM(2,4,5,7) = 2² · 5 · 7 = 140

Fracciones con mismo denominador:

3/5 = (3 · 7 · 4)/(5 · 7 · 4) = 84/140

4/7 = (4 · 5 · 4)/(7 · 5 · 4) = 80/140

3/4 = (3 · 5 · 7)/(4 · 5 · 7) = 105/140

1/2 = (1 · 2 · 5 · 7)/(2 · 2 · 5 · 7) = 70/140

Comparando:

70/140 < 80/140 < 84/140 < 105/140

  1/2     <     4/7  <     3/5    <     3/4

To learn more about trayecto visit: https://brainly.com/question/20802079

#SPJ1

The expression we get from the given functions h for all real numbers x.

h(-3)= 8

Given that,

All real numbers x are defined by the functions h.

h(x)= -x+5

We have to find the expression

h(-3)

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.

Take the functions,

h(x)= -x+5

Now, Take

h(-3) =-(-3)+5 = 3+5= 8

Therefore, The expression we get from the given functions h defined for all real numbers x.

h(-3)=8

To learn more about expression visit: brainly.com/question/14083225

#SPJ1

Answer:

slope: 4

Y intercept: -7

Step-by-step explanation:

slope intercept form is y=Mx+b

m- slope

b- y intercept

Looking at this equation where m is 4 is so the slope is 4

And where b is -7 is so the y intercept is -7

Hopes this helps please mark brainliest

The volume of the fully inflated balloon is 267.95 cubic inches, the volume of half-inflated balloon is 133.97 cubic inches and it's radius is 3.17in

The volume of sphere is the measure of space that can be occupied by a sphere. If we draw a circle on a sheet of paper, take a circular disc, paste a string along its diameter and rotate it along the string. This gives us the shape of a sphere.

The formula of a sphere is given as

v = 4/3πr³

But diameter = 2 * radius

radius = diameter / 2

radius = 8/2

radius = 4in

The volume of the fully inflated balloon will be

v = 4/3πr³

v = 4/3 * 3.14 * 4³

v = 267.95in³

The volume of the fully inflated balloon is 267.95in³

b) The volume of the half-inflated balloon will half the size of the current volume

v = 267.95in³ / 2 = 133.97in³

c) v = 4/3πr³

133.97 = 4/3 * 3.14 * r³

r = 3.17in

Learn more on volume of a sphere here;

https://brainly.in/question/30880094

#SPJ1

Answer:

incomplete question..please complete the question to get the answer. there are some missing details

a) The sampling proportion's mean value is 0.25. 0.016 is the standard deviation. The form resembles a bell.

b) There is a 10% possibility of getting this number, p=0.27 or more, given a sample proportion, so I wouldn't be surprised.

c) Since there is no chance that the sample fraction of 0.31 will occur, I would be shocked if it did.

Given,

a) The null hypothesis proportion would be the middle of the sampling distribution (p-0.25). So, p=0.25 is the sampling proportion's mean value.

This would be the standard deviation:

σp = √(p (1 - p) / n) = √(0.25 × 0.75/731) = 0.016

The distribution would resemble a binomial distribution, hence the form would be bell-shaped.

b) By calculating the z-value and checking for its probability in the standard normal distribution, we may determine the likelihood of a value p=0.27 in this distribution.

z = (p - π) / σp = (0.27 - 0.25) / 0.016 = 0.02/0.016  = 1.25

p(z > 1.25) = 0.106

There is a 10% probability of achieving this value, p=0.27 or more, for a sample proportion, so I wouldn't be surprised.

c) We repeat the calculation for p=0.31

z = (p - π) / σp = (0.31 - 0.25) / 0.016 = 0.06/0.016  = 5

p(z > 5) = 0.000

I would be astonished to see that value because the probability of this sample fraction occurring at p=0.31 is zero.

Learn more about probability here;

https://brainly.com/question/15727765

#SPJ4

Answer:

1.9

2.3

3.6

4.5

5.20

Step-by-step explanation:

hope it helps

The given equation is a combined variation.

We have been given an equation is

[tex]\frac{xy}{z}[/tex]

This is an equation in which we have three variables and one constant.

This can not be the case of direct or inverse variation because in direct or inverse variation we have only two variables. Whereas, here we have three variables.

So, Direct and inverse options are discarded.

So, either It can be joint or combined

In joint variation both the variables are directly proportional

Hence, given equation is not joint because if we rewrite the equation we will get [tex]y = \frac{cz}{x}[/tex] both the variables are not directly proportional.

In combined, one variable is directly proportional and the other one is inversely proportional.

From [tex]y = \frac{cz}{x}[/tex]  we can see that z is directly proportional and x is inversely proportional.

Hence the answer is, the given equation is combined variation.

To learn more about variations click here https://brainly.com/question/2375770

#SPJ9

For the given infinite geometric sequence,

(a) the two expressions for r are [tex]r=\frac{6}{m-1}[/tex] and [tex]r= \frac{m+8}{6}[/tex]

(b) The two possible values of m are -8 and 5.

(c) The two possible values of r are [tex]-\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex]

What are Geometric Series?

What is the Common Ratio of an Infinite Geometric Sequence?

In the question, the first three terms of an infinite geometric sequence are given as, m-1, 6, m+8

[tex]\implies a_{0} =m-1, a_{1}=6,[/tex] and [tex]a_{2}=m+8[/tex]

So, the common ratio is calculated as,

[tex]r=\frac{6}{m-1}=\frac{m+8}{6}[/tex]

Here, there are two expressions,

[tex]r=\frac{6}{m-1}[/tex]    ------(1), and  [tex]r= \frac{m+8}{6}[/tex]  ------(2)

Simplifying (1), we get

[tex]r(m-1)=6[/tex]  -----(3)

Simplifying (2), we get

[tex]6r=m+8\\\implies r= \frac{m}{6}+\frac{8}{6}[/tex]   ------(4)

Now, substituting the values of (4) in (3), we get

[tex](\frac{m}{6}+\frac{8}{6})(m-1)=6\\\implies \frac{m^{2} }{6}-\frac{m}{6} +\frac{2m}{3}-\frac{2}{3} =6\\\implies m^{2}+3m-4=36\\[/tex]

Solving further, we get

[tex]\implies m^{2}+3m-40=0\\\implies m=5, m=-8[/tex]

So, when [tex]m=5, r=\frac{6}{5-1}=\frac{3}{2}[/tex]

Also, when [tex]m=-8, r=\frac{6}{-8-1}=-\frac{2}{3}[/tex]

Therefore, (a) the two expressions for r are [tex]r=\frac{6}{m-1}[/tex] and [tex]r= \frac{m+8}{6}[/tex]

(b) The two possible values of m are -8 and 5.

(c) The two possible values of r are [tex]-\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex]

To learn more about common ratio from the given link

https://brainly.com/question/24643676

#SPJ1

The Hiking club will be 0.6.

The completion for the row of the table will be:

Grade 7

Dance club: 0.25

Hiking club: 0.75

Total : 1

Grade 8:

Dance club: 0.40

Hiking club: 0.60

Total : 1

How to calculate the values?

The dance club for grade 7 will be calculated as:

= Number of dancers / Total number

= 5/20

= 0.25

The hiking club will be:

= 15/20

= 0.75

The dance club for grade 8 will be calculated as:

= Number of dancers / Total number

= 20/50

= 0.4

The hiking club will be:

= 30/50

= 0.6

Hence, The Hiking club will be 0.6.

Learn more about Ratio at:

https://brainly.com/question/13419413

#SPJ1

The probability of rolling a yahtzee on the first round is calculated to be  6/46656 or 1/7776

Given that,

A dice is rolled for one time .

To find : The probability that a yahtzee will be rolled on the first round.

Your first die will be one of the 6 possible results 6/6 times

That will match on the second die 1/6th of the time.

The third, fourth, and fifth dice all share this characteristic.

Multiplying the all probabilities that the first die will be a yahtzee which is

P( yahtzee will be rolled on the first round) = Product of all possible outcomes of each time a dice is rolled.

6/6*1/6*1/6*1/6*1/6*1/6=6/46656 or 1/7776

Therefore, probability that a yahtzee will be rolled on the first round is 1/7776.

Learn more about probability here:

brainly.com/question/11234923

#SPJ4

The prime factorization of the number 68 is 2×2×17 and least prime number is 2 and greatest prime number is 17.

A number system is defined as a system of writing to express numbers.

We need to find the prime factorization of the number 68

Prime factorization is a process of writing all numbers as a product of primes.

The prime factorization of 68 is 2×2×17

The prime factors of 68 are 2 and 17.

The least prime number is 2 and greatest prime number is 17.

Hence the prime factorization of the number 68 is 2×2×17 and least prime number is 2 and greatest prime number is 17.

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ1

Check the picture below.

Answer:

Exterior angle: 86°

Base angle: 43°

Base angle: 43°

Third angle: 94°

Step-by-step explanation:

First we'll find x, then calculate all the angles.

There is a mark on two of the sides of the triangle. Two sides are the same. This is an isosceles triangle. So that means the base angles are the same also. One is marked 5x - 12, so the other base angle is also 5x - 12.

The marked exterior angle has a special relationship with the two remote interior angles.

If you add the two remote interior angles it equals the exterior angle.

8x-2 = 5x-12 + 5x-12

Combine like terms.

8x - 2 = 10x - 24

Subtract 8x.

-2 = 2x - 24

Add 24.

22 = 2x

Divide by 2.

11 = x

Now we can find all the angles.

The exterior angle is 8x - 2

= 8(11) - 2

= 88 - 2

= 86°

Base angle is 5x - 12

= 5(11) - 12

= 55 - 12

= 43°

The last angle in the triangle is a linear pair with the exterior angle. Or (Also,) the three angles in the triangle add up to 180°.

Angle+43°+43°=180°

Angle + 86 = 180

Angle = 94°