An escalator moves at the rate of 2 feet per second. At what rate does the escalator move in miles per hour? 5280 feet=1 mile

Answer:

a = -2

Step-by-step explanation:

f(x)=ax+b

f(2)=1  

f(-3)=11

f(2) = 1   means   2a+b =1

f(-3)=11   means   -3a + b = 11

Subtracting the two equations

-(-3a +b =11) becomes 3a -b = -11   so we can add

2a+b =1

3a - b = -11

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

5a = -10

Divide by 5

5a/5 = -10/5

a=-2

Answer:

The unit price of the 20 pack is $0.79 and the unit price for the 8 pack is $0.80.

Step-by-step explanation:

Simply Take the price of the pack of batteries divided by the number within the pack.

$6.40 / 8 == $0.80

$15.80 / 20 == $0.79

Cheers.

The question is incomplete. You can find the missing content below.

A package of 8-count AA batteries costs $6.40. A package of 20-count Of batteries costs $15.80. Which statement about the unit prices is true?

A) The 8-count pack of AA batteries has a lower unit price of $0.79 per battery.

B) The 20-count pack of AA batteries has a lower unit price of $0.80 per battery.

C) The 8-count pack of AA batteries has a lower unit prices of $0.80 per battery.

D) The 20-count pack of AA batteries has a lower unit price of $0.79 per battery.

The correct option is Option D: The 20-count pack of AA batteries has the lower price of $0.79 per battery.

Inequality is the relation between two numbers or variables or expressions showing relationships like greater than, greater than equals to, lesser than equals to, lesser than, etc.

For example 2<9

A package of 8-count AA batteries has cost = $6.40.

cost per unit count AA batteries will be= total cost of AA batteries/ number of AA batteries

= $6.40/8= $0.8

A package of 20-count AA batteries has cost = $15.80.

cost per unit count AA batteries will be= total cost of AA batteries/ number of AA batteries

= $15.80/20= $0.79

As 0.79<0.8

cost of 20-count AA batteries <  cost of 8-count AA batteries

Therefore the correct option is Option D: The 20-count pack of AA batteries has the lower price of $0.79 per battery.

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Answer: The value of [tex](g - f)(x)=4 .[/tex]

Step-by-step explanation:

Given functions :  [tex]f(x) = x + 4[/tex] and [tex]g(x) = x + 7[/tex]

To find : [tex](g - f)(x)[/tex]

Difference between two functions: [tex](u-v)(x)=u(x)-v(x)[/tex]

Then, [tex](g-f)(x)=g(x)-f(x)[/tex]

[tex]=(x+7)-(x+4)=x+7-x-4\\\\=7-4=3[/tex]

Hence, the value of [tex](g - f)(x)=4 .[/tex]

Answer:

(2-j)(4-y)

Step-by-step explanation:

Factoring using grouping,

(2-j)(4-y)

Answer:

1 box of 20 and 1 box of 14

They will cost $410

Step-by-step explanation:

1. Find how many boxes of 20 DVD movies can be bought

415 - 240 = 175

1 box of 20 DVD movies can be sold

2. Find how many boxes of 14 DVD movies can be bought from $175

175 - 170 = 5

1 box of 14 DVD movies can be bought

3. Find the cost

240 + 170 = 410

Step-by-step explanation:

Pythagoras Theorem

If the sum of the squares of the smaller two sides is equal to the square if the third side then it is a right triangle

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

So, (5)^2 + (12)^2

is 25 + 144 = 169

Which is equal to (13)^2 which is also 169

The sides of the given triangle follows pythagoras theorem, therefore it is a right triangle

Hope it helps:)

Answer:

Pythagorean theorem

Step-by-step explanation:

We can explain it using  the Pythagorean theorem. Right triangles always have a hypotenuse which is the longest side. That means 13 must be the hypotenuse of the triangle. The Pythagorean theorem is a^2+b^2=c^2

We already know all the values since every side is given so we just fill it in.

5^2+12^2=13^2

25+144=169

169=169

It is a right triangle

Answer:

Step-by-step explanation:

2a is the middle term of a quadratic expression.  2 is the coefficient of a to the first power.

Not much more you can say about this.

Please, if the original question includes answer choices, share those choices.  Thank you.

Answer:

45

62x

______

  90

2700+

_________

2790

Step-by-step explanation:

Answer:

[tex]X=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]

Step-by-step explanation:

We are given the following matrix equation, from which we have to isolate X and simplify this value.

[tex]\begin{bmatrix}2&4\\ \:\:\:5&4\end{bmatrix}X\:+\:\begin{bmatrix}-8&-8\\ \:\:\:12&1\end{bmatrix}=\:\begin{bmatrix}-10&6\\ \:\:\:25&24\end{bmatrix}[/tex]

To isolate X, let us first subtract the second matrix, as demonstrated below, from either side. Further simplifying this equation we can multiply either side by the inverse of the matrix being the co - efficient of X, isolating it in the doing.

[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}[/tex] (Simplify second side of equation)

[tex]\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}=\begin{bmatrix}\left(-10\right)-\left(-8\right)&6-\left(-8\right)\\ 25-12&24-1\end{bmatrix}=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] ,

[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] (Multiply either side by inverse of matrix 1)

[tex]X=\begin{bmatrix}2&4\\ 5&4\end{bmatrix}^{-1}\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]

Our solution is hence option c

Answer:

b ≈ 9.5, c ≈ 14.7

Step-by-step explanation:

Using the Sine rule in Δ ABC, that is

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values

[tex]\frac{7}{sin23}[/tex] = [tex]\frac{b}{sin32}[/tex] ( cross- multiply )

b × sin23° = 7 × sin32° ( divide both sides by sin23° )

b = [tex]\frac{7sin32}{sin23}[/tex] ≈ 9.5 ( to the nearest tenth )

Also

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]

[tex]\frac{7}{sin23}[/tex] = [tex]\frac{c}{sin125}[/tex] ( cross- multiply )

c × sin23° = 7 × sin125° ( divide both sides by sin23° )

c = [tex]\frac{7sin125}{sin23}[/tex] ≈ 14.7 ( to the nearest tenth )

Answer:

Hey there!

The third graph, with a maximum at (-1, -3) is the correct choice.

Let me know if this helps :)

Answer:

see below

Step-by-step explanation:

f(x) = –(x + 1)^2 – 3

We know that this is a parabola in the form

y = a( x-h)^2 +k

where ( h,k) is the vertex

y = -1( x- -1)^2 + -3

a is negative so the parabola opens downward

( -1,-3) is the vertex

Answer: You will need 8 cup scales

Step-by-step explanation:

kg=1000 grams

2000/250=8

It is possible to measure 2 kilograms or 2000 grams in 8 cups, it is not possible to measure in three weighs.

Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

The percentage is defined as the ratio expressed as a fraction of 100.The percentage is denoted by sign of %.For example, if XYZ scored 46% marks in his test, it means that he scored 46 marks out of 100. It is written as 46/100 in the fraction form and 46:100 in terms of ratio.

Given data as :

9kg of oats and cup scales that gears of 50g and 200g.

Total oats need to measure = 9kg

Since, 1 kg contains 1000 grams.

1 kg = 1000 grams

2kg = 2000 grams

9kg = 9000 grams

Cup scales that gears as 50g and 200g

The number of one cup contains in gram = 200 + 50 = 250

The number of cups, considering that each cup weighs 250 grams.

The number of cups = 2000/250

The number of cups = 8

Hence, while it is possible to measure 2 kilograms or 2000 grams in 8 cups, it is not possible to measure in three weighs.

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Answer:

A. 1

B. -1

C. -1.67

D. 0.67

E. 3.33

Step-by-step explanation:

Mathematically;

z-score = (x-mean)/SD

From the question, mean = 20 , SD = 3 while x represents the individual values

A. 23

Z = (23-20)/3 = 3/3 = 1

B. 17

z = (17-20)/3 = -3/3 = -1

C. 15

z = (15-20)/3 = -5/3 = -1.67

D. 22

z = (22-20)/3 = 2/3 = 0.67

E. 30

z = (30-20)/3 = 10/3 = 3.33

Answer:

[tex]\boxed{\frac{984}{1000}}[/tex]

Step-by-step explanation:

Hey there!

Well .984 is 984 over 1000 so .984 as a fraction is 984/1000.

We can check this by doing 984 / 1000 which is .984.

Hope this helps :)

Answer:

  A. rectangle

  B. any of triangle, quadrilateral, pentagon, hexagon

Step-by-step explanation:

A. A plane perpendicular to the base will intersect 2 adjacent or 2 opposite lateral faces, as well as the two bases. Each plane intersected will result in an edge of the cross sectional figure. The figure will have two pairs of parallel edges, so is a rectangle.

__

B. If the intersecting plane is not constrained to be perpendicular to the base(s), it can intersect 3, 4, 5, or all 6 faces of the prism. Hence, the shape of the cross section can be any of ...

Answer:

6x + 6 = 32

6x = 32 - 6

6x = 26

divide both sides by 6

6x/6 = 26/6

6x + 6 = 4.35

9x - 9 = 24

9x = 24 + 9

9x = 33

divide both sides by 9

9x/9 = 24/9

9x + 9 = 2.66

9x + 9 = 2.66

Answer: x=3

Step-by-step explanation:

[tex]\frac{32}{24} =\frac{4}{3} \\\\\frac{4}{3}=\frac{6x+6}{9x-9}\\ x=3[/tex]

Answer:

Step-by-step explanation:

probabilty distribution= interval of x/total area of the distribution

OR  P(x)= frequency of x/total frequency(N)*the interval of x(w)

x                   f                   probabilty f/N*w

16                 10                  0.2

17                  16                  0.32

18                  20                  0.4

19                    4                   0.08

w is the width of the bar( interval) 17-16=1

N=10+16+20+4=50

( only need to draw histogram)

Let the largest integer equal x, the 3rd number ( smallest-number) would be x - 2

The sum of the two would be:

X + 5(x-2) = -244

Simplify:

X + 5x -10

Combine like terms

6x -10 = -244

Add 10 to both sides:

6x = -234

Divide both sides by 6

X = -234/6

X = -39

The smallest number is x-2 = -39-2 = -41

The answer is -41

Answer:

1). [tex]\frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}[/tex]

2). [tex]\frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}[/tex]

Step-by-step explanation:

In this question we have to write the fractions in the factored form.

Rational expressions are [tex]\frac{2}{x^{2}-x-12 }[/tex] and [tex]\frac{1}{x^{2}-16 }[/tex].

1). [tex]\frac{2}{x^{2}-x-12 }[/tex]

Factored form of the denominator (x² - x - 12) = x² - 4x + 3x - 12

                                                                           = x(x - 4) + 3(x - 4)

                                                                           = (x + 3)(x - 4)

Therefore. [tex]\frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}[/tex]

2). [tex]\frac{1}{x^{2}-16 }[/tex]

Factored form of the denominator (x² - 16) = (x - 4)(x + 4)

[Since (a²- b²) = (a - b)(a + b)]

Therefore, [tex]\frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}[/tex]

Answer:

129 m/s^2

Step-by-step explanation:

The length of a rectangle is increasing at a rate of 9m/s

dL/dt = 9m/s

The width is increasing at a rate of 7m/s

dw/dt= 7m/s

The formular for solving the area of a rectangle is length × width

Therefore, to calculate how fast the rectangle is increasing we will apply the product rule

dA/dt= L × dw/dt + W × dl/dt

= 12×7 + 5×9

= 84+45

= 129m/s^2

Hence the area of the rectangle is increasing at 129m/s^2

Answer:

[tex]area = \pi {r}^{2} \\ r = 7 \\ a = \frac{22}{7} \times {7}^{2} [/tex]

[tex]a = \frac{22}{7} \times 49 \\ a = 22 \times 7 = 154 {cm}^{2} [/tex]

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ a \: = 3.14 \times {7}^{2} \\ a \: = 3.14 \times 49 = 153.86 {cm}^{2} [/tex]

Answer:

C. 153.86 in^2

Step-by-step explanation:

The area of a circle can be found using the following formula.

[tex]a=\pi r^2[/tex]

where r is the radius.

We know the radius is 7 inches. Therefore, we can substitute 7 in for r.

[tex]r= 7 in[/tex]

[tex]a=\pi (7 in)^2[/tex]

Evaluate the exponent.

(7 in)^2= 7 in * 7 in= 49 in^2

[tex]a= \pi * 49 in^2[/tex]

Let's use 3.14 for pi.

[tex]a= 3.14 * 49 in^2[/tex]

Multiply 3.14 and 49

3.14 * 49=153.86

[tex]a= 153.86 in^2[/tex]

The area of the circle is 153.86 square inches. Therefore, C is the correct answer.

Answer:

[tex] \boxed{\sf Instantaneous \ velocity \ (v) = -3} [/tex]

Given:

Relation between position of an object at time t is given by:

s(t) = -9 - 3t

To Find:

Instantaneous velocity (v) at t = 8

Step-by-step explanation:

To find instantaneous velocity we will differentiate relation between position of an object at time t by t:

[tex] \sf \implies v = \frac{d}{dt} (s(t))[/tex]

[tex] \sf \implies v = \frac{d}{dt} ( - 9 - 3t)[/tex]

Differentiate the sum term by term and factor out constants:

[tex] \sf \implies v = \frac{d}{dt} ( - 9) - 3 (\frac{d}{dt} (t))[/tex]

The derivative of -9 is zero:

[tex] \sf \implies v = - 3( \frac{d}{dt} (t)) + 0[/tex]

Simplify the expression:

[tex] \sf \implies v = - 3( \frac{d}{dt} (t))[/tex]

The derivative of t is 1:

[tex] \sf \implies v = - 3 \times 1[/tex]

Simplify the expression:

[tex] \sf \implies v = - 3 [/tex]

(As, there is no variable after differentiating the relation between position of an object at time t by t so at time t = 8 is of no use.)

So,

Instantaneous velocity (v) at t = 8 is -3

Answer: Honeymoon2871

Step-by-step explanation:

Answer:

[tex]\huge \boxed{x=3}[/tex]

Step-by-step explanation:

[tex]6(x+2)=30[/tex]

[tex]\sf Divide \ both \ sides \ by \ 6.[/tex]

[tex]x+2=5[/tex]

[tex]\sf Subtract \ 2 \ from \ both \ sides.[/tex]

[tex]x=3[/tex]

Answer:

3

Step-by-step explanation:

30 = 6(x+2)

30/6 = 5

5 = x+2

5-2 = 3

3=x

This is a pretty simple question and I tried to make it as simple as possible when explaining it.

Answer:

(x+4)/3. When x is 5 the answer is 3

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Step-by-step explanation:

Suppose, John walks with a speed x

Then, John can jog at a speed 2x

[tex]total \: time \: = \frac{total \: distance}{average \: speed} [/tex]

TOTAL TIME

[tex]0.9 = \frac{5}{2x} + \frac{2}{x} [/tex]

Further solving :

x = 5 mph

Average jogging speed (2x) = 10 mph

Answer:

10mph

Step-by-step explanation:

We know that John's total trip is 0.9 hours, so let's try to figure out how much of that time is spent jogging, and how much of it is spent walking.

We can do that by naming the time he takes to jog a mile y.

An equation would be:

5y+2(2y)=0.9

5y+4y=0.9

y=0.1

It takes him 0.1 hours, or 6 minutes to jog a mile.

Since he jogged 5 miles, his jogging time is 0.5 hours, or 30 minutes.

Now,

Let's name the speed he jogs x (miles per hour)

This allows us to set up another equation.

Note that:

Speed=distance/time

His jogging speed is x.

x=5/0.5

x=10

His average jogging speed is 10 miles an hour.

Hey there! I'm happy to help!

We want to find the equation of a line in y-intercept form, which is y=mx+b, where x and y are a point on the line, m is the slope, and b is the y-intercept.

We already know that our slope is -3.

y=-3x+b

We want to solve for b now. We can plug in our point (-9,-9) to solve for it.

-9=-3(-9)+b

-9=27+b

b=-36

So, our equation is y=-3x-36.

I hope that this helps! Have a wonderful day! :D

Answer:

A typical example would be when a statistician wishes to estimate the ... by the standard deviation ó) is known, then the standard error of the sample mean is given by the formula: ... The central limit theorem is a significant result which depends on sample size. ... So, the sample mean X/n has maximum variance 0.25/ n.

Step-by-step explanation: