Evaluate and simplify the following complex fraction

70 beats per minute

24*60=1440 minutes in one day

70*1440=100,800 beats per day

Answer:

The number of minutes per day is 60 × 24 = 1440 (minutes)

Since we know that human heart beats about 70 times every minute, the number of times the human heart beats in one day should be:

70 × 1440 = 100800 (times)

Answer:

[tex]\large\boxed{\left\{x\ |\ x<\dfrac{6}{7}\right\}}[/tex]

Step-by-step explanation:

[tex]\dfrac{7x}{3}<2\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{7x}{3\!\!\!\!\diagup_1}<3\cdot2\\\\7x<6\qquad\text{divide both sides by 7}\\\\\dfrac{7x}{7}<\dfrac{6}{7}\\\\x<\dfrac{6}{7}[/tex]

Answer: First Option

{[tex]x|x<\frac{6}{7}[/tex]}

Step-by-step explanation:

We have the following inequality [tex]\frac{7}{3}x <2[/tex]

To solve the inequality, apply the following steps:

1) Multiply by 3 on both sides of the inequality

[tex]\frac{3 * 7}{3}x <2 * 3\\\\7x <6[/tex]

2) Divide by 7 both sides of the inequality

[tex]\frac{7}{7}x <\frac{6}{7}[/tex]

[tex]x <\frac{6}{7}[/tex]

The solution is all numbers smaller than [tex]\frac{6}{7}[/tex]

The correct choice is the second one which is 4(2 + y)

Answer:

4(2 + y)

Step-by-step explanation:

Potential Energy: the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors.Compare with kinetic energy

Friction :the action of one surface or object rubbing against another.

plz dont sue me if Im wrong

The wheelie chair stops moving because of friction between the chair wheels and the floor, along with a bit of air resistance. These forces oppose the motion and gradually slow the chair down until it stops.

Izzy's dog is 10.32 years older.

10.5 years - 0.18 years = 10.32

Answer:

31. (a) The height decreases by 12 feet each second towards the first floor

(b)

(c) It takes 15 seconds for the elevator to get to the first floor

(d) The basement floor is 48 feet below the first floor

Step-by-step explanation:

31 (a) explanation:

An elevator is 180 feet above the first floor.

Each second, it descends 12 feet.

So the elevator's change in height each second is a decrease of 12 feet towards the first floor.

31 (b) explanation:

If the elevator goes down 12 feet, towards the first floor, in 1 second then;

31 (c) explanation:

If the elevator is 180 feet above the first floor and it takes 1 second to descend 12 feet,

Then it will take: [tex]\frac{180 feet}{12 feet}[/tex] × 1 second = 15 seconds reach the first floor.

31 (d) explanation:

From the first floor it takes 4 seconds to reach the basement floor

Therefore the basement floor is [tex]\frac{4 seconds}{1 second}[/tex] × 12 feet = 48 feet below the first floor

The integer -12 is the change in the height of the elevator per second

It will take 15 seconds for the elevator to get to the first floor.

The height of the basement floor with respect to the first floor is 48 feet.

Since the elevator descends, the change in height is negative.

The magnitude of the change in height is 12 feet per second, so the change in height is −12 feet per second.

The completed table is

Time Height

0 sec 180

3 sec 180-3*12=132

6 sec 180-6*12=108

9 sec 180-9*12=72

Here, we divide the initial height by the rate of descent.

So, we have

Time = 180 feet / 12 feet per second = 15 seconds.

If the elevator descends to the basement floor in 4 seconds, then the height of the basement floor with respect to the first floor is

4 seconds * 12 feet per second = 48 feet.

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Answer:

The image of p is (2.5x , 2.5y)

Step-by-step explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.  

- It can become larger or smaller, but the shape of the

 figure does not change.  

- The scale factor, measures how much larger or smaller  

 the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

* In our problem

- Point p is (x , y)

- Center of dilation is (0 , 0)

- The scale factor is 2.5

* To get the image multiply each coordinates of p by 2.5

∴ The image of p is (2.5x , 2.5y)

Answer: The answer is 3/4

Step-by-step explanation:

I think it’s B.

I did 9 times 7

The area is going to be 63

Answer:

She can give 1/8 of a box to 40 people

5x8=40

Step-by-step explanation:

Terri can give seeds to 40 people, each receiving 1/8 of a box, as she has a total of 40 portions of 1/8 from her 5 boxes of flower seeds.

Terri has 5 boxes of flower seeds and wants to know how many people she can give seeds to if she gives away 1/8 of a box to each person. To solve this, we calculate the total portions of seeds she has and then divide that by the portions she is giving to each friend. Since there are 8 portions of 1/8 in one box, Terri has a total of 5 boxes  imes 8 = 40 portions of seeds. Hence, Terri can give seeds to 40 people, with each person receiving 1/8 of a box.

y=2x

switch x and y

x=2y

solve for y

x/2 =y

this is the same as g(x)

Answer:

see explanation

Step-by-step explanation:

If f(x) and g(x) are inverses then

f(g(x)) = g(f(x)) = x

f(g(x)) = f([tex]\frac{x}{2}[/tex]) = 2 × [tex]\frac{x}{2}[/tex] = x

g(f(x)) = g(2x) = [tex]\frac{2x}{2}[/tex] = x

Hence

f(x) and g(x) are inverse functions

Answer:

113.51

Step-by-step explanation:

Answer:

4 1/10 kg

Step-by-step explanation:

To find the total mass, we add the mass of the three baskets

1 1/10 + 1 3/10 + 1 7/10

Since they have the same denominator

 1   1/10

 1   3/10

 1   7/10

-------------

 3  11/10

Change the improper fraction to a mixed number

11/10 = 1 1/10

3 + 1 1/10

4  1/10

Answer:Exact form: 5/2

Decimal form: 2.5

Mixed number form: 2 1/2  

Hope this helps:)

Step-by-step explanation:

Answer: C. 390

Step-by-step explanation:

Firstly, we need to find the amount each of the categories.

House: 6500 * 0.25 = 1625

Bills: 6500 * 0.14 = 910

Food: 6500 * 0.19 = 1235

Other: 6500 * 0.42 = 2730

All of those add up to 6500.

House - Food

1625 - 1235 = 390

Without the specific percentages from the circle graph representing housing and food, we can't determine the exact dollar difference. But theoretically, we would multiply each percentage by the total budget ($6500) and subtract the food from the housing amount.

Without actual percentages or numbers for the family's expenditures on housing and food provided in the circle graph, we cannot determine the exact dollar amount difference. However, we can explain theoretically how you would do it with actual values. After identifying the percentages represented by housing and food on the graph, you would multiply each percentage by the total monthly budget of $6,500. Subtract the amount spent on food from the amount spent on housing to get the difference. Based on the choices given, it seems you want help in selecting the correct option. If you provide the specific percentages from the graph, I will gladly assist further in your mathematical problem.

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Answer:

Median is the middle number

Mean is the average

Step-by-step explanation:

for #4

order the tree heights from the least to greatest and the middle number would be your median. If you have an even amount (no middle) then add the two middle numbers and dived it by 2

for # 5

Add the numbers all up on a calculator then dived by the amount of numbers you added.

Really simple :)

Hope that helps!

Answer:

Step-by-step explanation:

The median is 73.5

The mean is 72.7

Hope this helps!

Answer:

37/40

Step-by-step explanation:

Answer:

0.345%

Step-by-step explanation:

you multiply is by 100

Answer:

A

Step-by-step explanation:

When converting from a decimal to a percent, you always multiply the decimal by 100, and in this case, multiplying the number 0.00345 gets us 0.345. This number is the percent, in this case 0.345%, or answer choice A.

Answer:

The length of OA = 10 cm

Step-by-step explanation:

* Lets revise some facts about the circle

- If two tangents drawn from a point outside the circle, then

 they are equal in lengths

- The radii of the circle are perpendicular to the tangents at the

 point of tang-ency

- The line from the center to the angle between the two tangents

 bisects it

* Now lets solve the problem

∵ The sides of ∠A are tangents to circle O

∴ The radius of the circle O ⊥ to the tangent at the point of tang-ency

∴ The line OA bisects ∠A

- The measure of ∠A = 60°

∴ The measure of the angle between line OA and the tangent

  is equal to 1/2 × 60° = 30°

* Now we have right angle triangle formed from the line OA as a  

 hypotenuse two legs of the right angle one of them is the

 tangent and the other is the radius

∵ r = 5 cm

∵ The measure of the angel opposite to r is 30°

∵ OA is the hypotenuse

- By using trigonometry function

∴ sin(30°) = 5/OA

∵ sin(30°) = 1/2

∴1/2 = 5/OA ⇒ by using cross multiplication

∴ OA = 2 × 5 = 10 cm

* The length of OA = 10 cm

*Image Linked Below*

Answer:

x=7*64/80

x=5.6

Step-by-step explanation:

Let x represent miles would she run in 64 minutes?

Question Sets Up the Proportion

70/80=x/64     |Cross Multiplying to solve for x

     x = 7*64/80

     x = 5.6mi

Answer:

He would run 5 miles. If you divide 80 by 7, it would equal 11. Meaning subtract 11 for every mile. To get to 64 subtract 11 twice. That leaves 58. 58 would be 5 miles. 11+11+11+11+11 is 55. 3 more minutes and its 58. Our total is 5 miles.

Hope this helped. Have a good day. :D

Also let me know if you need more help.

Step-by-step explanation:

Answer: 1. Yellow, green, black, white, blue, red. yes equally likely

2. heads, tails. yes equally likely

3. possibilites: yellow heads, yellow tails, green heads, green tails, black heads, black tails, white heads, white tails, blue heads, blue tails, red heads, red tails.

4. 1/12

5. still 1/12

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Using the trigonometric identities

• cscx = [tex]\frac{1}{sinx}[/tex] and secx = [tex]\frac{1}{cosx}[/tex]

Consider the left side

cscx sec x = [tex]\frac{1}{sinx}[/tex] × [tex]\frac{1}{cosx}[/tex] = [tex]\frac{1}{sinxcosx}[/tex]

Consider the right side

2 csc2x = [tex]\frac{2}{sin2x}[/tex] = [tex]\frac{2}{2sinxcosx}[/tex] = [tex]\frac{1}{sinxcosx}[/tex]

left side = right side hence identity is verified

I guess you mean [tex]\cos a=-\dfrac25[/tex]. Since [tex]a[/tex] is in quadrant III, we expect [tex]\sin a<0[/tex]. Then

[tex]\sin a=-\sqrt{1-\cos^2a}=-\dfrac{\sqrt{21}}5[/tex]

Since [tex]b[/tex] is in quadrant I, we expect [tex]\sin b>0[/tex], so that

[tex]\sin b=\sqrt{1-\cos^2b}=\dfrac{\sqrt{15}}4[/tex]

Now,

[tex]\sin(a+b)=\sin a\cos b+\cos a\sin b=-\dfrac{2\sqrt{15}+\sqrt{21}}{20}[/tex]

[tex]\cos(a+b)=\cos a\cos b-\sin a\sin b=\dfrac{3\sqrt{35}-2}{20}[/tex]

and

[tex]\tan(a+b)=\dfrac{\sin(a+b)}{\cos(a+b)}=-\dfrac{2\sqrt{15}+\sqrt{21}}{3\sqrt{35}-2}[/tex]

Answer:

[tex]a=-2\\b=4\\c=-3[/tex]

Step-by-step explanation:

In a quadratic equation in the Standard form

[tex]ax^2+bx+c=0[/tex]

You need to remember that "a", "b" and "c" are the numerical coefficients (Where "a" is the leading coefficient and it cannot be zero: [tex]a\neq0[/tex]).

You can observe that the given quadratic equation is written in the Standard form mentioned before. This is:

[tex]-2x^2+4x-3=0[/tex]

Therefore, you can identify that the values of "a", "b" and "c" are the following:

[tex]a=-2\\b=4\\c=-3[/tex]

Answer:

a = -2

b = 4 and

c = -3

Step-by-step explanation:

A standard form of a quadratic equation is

ax₂ + bx + c = 0, where a, b and c are coefficients

To find the value of a, b, and c

The given equation is -2x² + 4x - 3 = 0

The degree of equation is 2, therefore it is a quadratic equation.

here a = -2, b = 4 and c = -3

Answer:

not sure, not enough info given

Step-by-step explanation:

what to do is

sin 45=AC/BC

or

cos 45=AB/BC

or

tan 45=AC/AB

2...bigger =3/5 less 1/8

To write the correct comparison symbol, we compare two numbers or expressions to determine their relationship, using <, >, or =. This mathematical skill is important for understanding and working with inequalities.

To answer a question that asks you to write the correct comparison (using <, >, or =), we need to evaluate and compare the given numbers or expressions to determine which symbol is appropriate. This involves mathematical understanding and skills such as ordering numbers, understanding inequalities, and applying mathematical operations if needed.

Let's use an example to illustrate this:

Writing the correct comparisons is an essential math skill that helps students understand and work with inequalities and is widely applicable in various aspects of both academics and real life.

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Answer:

Step-by-step explanation:

binomial

Answer:

polynomial

Step-by-step explanation:

A monomial has only 1 term ( mono - 1 )

A binomial has 2 terms ( bi - 2 )

A trinomial has 3 terms ( tri - 3 )

7x³ + 2x² - 9x + 1 ← has 4 terms and is a polynomial

Answer:

1 cupcake = $3.75

1 ice-cream = $4.50

1 doughnut = $1.50

Step-by-step explanation:

2 ice-cream + 1 cup cake = $12.75 ------------ [ 1 ]

1 ice-cream + 2 doughnuts = $7.50 ------------ [ 2 ]

1 cup cake + 1 doughnut + 1 ice-cream = $9.75 ------------ [ 3 ]

From [ 1 ] :

2 ice-cream + 1 cup cake = $12.75

1 cupcake = $12.75 - 2 ice-cream

Substitute [ 1 ] into [ 3 ]:

1 cup cake + 1 doughnut + 1 ice-cream = $9.75

$12.75 - 2 ice-cream + 1 doughnut + 1 ice-cream = $9.75

1 doughnut - 1 ice-cream = -$3  ------------ [ 4 ]

[ 2 ] + [ 4 ] :

3 doughnuts = $4.75

1 doughnut = $1.50

Substitute (1 doughnut = $1.50) into [ 2] :

1 ice-cream + 2 doughnuts = $7.50

1 ice-cream + 2 x $1.50 = $7.50

1 ice-cream + $3 = $7.50

1 ice-cream = $4.50

Substitute (1 ice-cream = $4.50) into [ 1 ]:

2 ice-cream + 1 cup cake = $12.75

2 x $4.50 + 1 cup cake = $12.75

1 cupcake = $12.75 - $9

1 cupcake = $3.75

To find the cost of each in a system of equations, you need to solve the equations simultaneously. You can solve for one variable first and substitute it into the other equation to find the value of the second variable. Once you have the value of one variable, you can substitute it back into one of the original equations to find the value of the other variable.

In the field of Mathematics, specifically in algebra, a system of equations is a set of equations with the same variables. When you're asked to find the cost of each one, you're actually being asked to solve this system of equations. Let's assume your system of equations is:

You can solve for one variable first from either equation and substitute it into the other. For example, from Equation 1 you can solve for x: x = (40 - 2y)/5. Substituting x into Equation 2 gives us: 3((40 - 2y)/5) + 4y = 35. Solving this will give you the value of y which can then be substituted into any of the original equations to find the cost of x.

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Answer:

it is 144.

I think.

The measure of angle 5 would be equal to 36°.

We know that for two similar figures, the pair by pair similar angles of those two similar figures are called corresponding angles. They are of same measurement.

Since straight angle is a 180-degree angle.

Now,

From the figure, we can see that line a and b are parallel to each other.

m∠1=36°

Therefore, m∠1= m∠5

This makes the angle corresponding to each other.

Hence, m∠5=36°

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Answer:

9 movies

Step-by-step explanation:

If we let the number of movies watched is "x",

Duke's total cost:

111.60 + 4x

Tenneshia's total cost:

16.40x

Since, the cost needs to be equal, we equate both their equations and solve for x, the number of movies at which they will have paid the same amount. Thus:

111.60 + 4x = 16.40x

111.60 = 16.40 x - 4x

111.60 = 12.40 x

x = 111.60/12.40 = 9

Hence, after 9 movies, they will have paid the same amount.

Answer is 9 movies

n = no. of movies

111.6 +4n= 16.4 n

116.4= (16.4-4)n

116.4 = 12.4 n

n = 116.4/12.4

n = 9 movies