An 8-oz bottle of hair spray costs $4.46. Find the unit price in cents per ounce

Answer:

m(x) is a dilation of scale factor K = 1/5 of f(x).

Step-by-step explanation:

The transformation is a horizontal dilation

The general transformation is defined as:

For a given function f(x), a dilation of scale factor K is written as:

g(x) = f(x/K)

If K > 1, then we have a dilation (the graph contracts)

if 0 < K < 1, then we have a contraction (the graph stretches)

Here we have m(x) = f(5*x)

Then we have a scale factor:

K = 1/5

So this is a contraction.

Then the transformation is:

m(x) is a dilation of scale factor K = 1/5 of f(x).

Answer:

An equation in the slope-intercept form is:

y = a*x + b

Where a is the slope, and b is the y-intercept.

a)

Here we have a slope of 6 and a y-intercept of -3

Then the equation is:

y = 6*x - 3

Now we want to graph this.

To graph it, we first need to find two points (x, y) that belong to this equation, then we can graph the points, and connect them with a line.

To find the points, we evaluate in two different values of x.

x = 0

y = 6*0 - 3 = -3

Then we have the point (0, -3)

x = 1

y = 6*1 - 3 = 3

Then we have the point (1, 3)

The graph of this line can be seen in the image below (the red one)

b) Similar to before, here the slope is -3/5, then the equation is something like:

y = (-3/5)*x + b

Now we also know that the line passes through the point (-10, 8)

This means that when x = -10, we must have y = 8

Replacing these two in the equation we get:

8 = (-3/5)*-10 + b

8 = 6 + b

8 - 6 = 2 = b

Then this equation is:

y = (-3/5)*X + 2

The graph can be found in the same way as before, the graph of this function can also be seen in the image below (the green one)

Answer:

The first one

Step-by-step explanation:

You just need to find the slope in the average of all the dots.

Answer:

the first option, y=3/7x-3

Step-by-step explanation:

the scatterplot begins around y=-3, so therefore the y-intercept is -3. The slope is obviously not higher than 1, so it is y=3/7x-3.

Answer:

24/145

Step-by-step explanation:

Trigonometric identities are equalities involving trigonometric functions and remains true for entire values of the variables involved in the equation.

Some trigonometric identities are:

sin(a + b) = sinacosb + cosasinb; sin(a - b) = sinacosb - cosasinb

cos(a + b) = cosacosb - sinasinb; cos(a - b) = cosacosb + sinasinb

Given that sin a = 3/5. sin a = opposite/hypotenuse.

Hence opposite = 3, hypotenuse = 5. using Pythagoras:

hypotenuse² = opposite² + adjacent²

5² = 3² + adjacent²

adjacent² = 16

adjacent = 4

Given that sin a = 3/5. a = sin⁻¹(3/5) = 36.86

cos a = cos 36.86 = 4/5

cos b = -20/29; b = cos⁻¹(-20/29) = 133.6

sinb = sin(133.6) = 21/29

sin(a + b) = sinacosb + cosasinb = (3/5 * -20/29) + (4/5 * 21/29) = -12/29 + 84/145

sin(a + b) = 24/145

Answer:

The 14-ounce bottle is the better deal

Step-by-step explanation:

I know this beause inorder to figure out which one is better you have to make them the same price and then see which bottle has more ounces. So I made each price 1$ so there is 1.58-ounces per dollar in the 5-ounce bottle and 1.17 -ounces per dollar in the 14-ounce bottle.

Answer:

yes

Step-by-step explanation:

but I can't see them here

Answer:

Yes it is very good for establishing identities.

Step-by-step explanation:

Since its a very preferable start it is a very good way to establish identity.

Answer:

Should be 5 1/2 if thats on there

Step-by-step explanation:

u take 11/2 and take out the 1 u get 10/2 so u cut 10 in half get 5 then add the one and make it 5 1/2

Answer:

D. 34

Step-by-step explanation:

Because this is a right triangle we can use sin, cos, tan.

Use cosine because the values of the adjacent side and hypotenuse are already given.

cos(θ) = 72/87

Because we are solving for the angle measure (and not the measure of the side) we need to use inverse cos.

cos⁻¹ = 72/87

put into a calculator and answer is approximatelyn34 degrees.

Answer:

7π/4 radians = 315°, Quadrant IV

sin(315°) = -√2/2

cos(315°) = √2/2

tan(315°) = -1

Step-by-step explanation:

Answer:

21/8x

Step-by-step explanation:

10x -20 = -6x+22

+6x-20 = 22

16x-20 = 22

16x +20= +20

16x/16x = 42/16x

x = 21/8x

Answer:

The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

How fast is the volume increasing:

To find this, we have to differentiate the variables of the problem, which are V and r, implicitly in function of time. So

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

The radius of a sphere is increasing at a rate of 2 mm/s.

This means that [tex]\frac{dr}{dt} = 2[/tex]

How fast is the volume increasing (in mm3/s) when the diameter is 100 mm?

Radius is half the diameter, so [tex]r = \frac{100}{2} = 50[/tex]

Then

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt} = 4\pi (50)^2(2) = 62832[/tex]

The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.

Explanation:

The Ø​ means "empty set". It's the set with nothing inside it, not even 0.

We can write Ø​ as { } which is a pair of curly braces with nothing between them.

The rule is that if we union any set A with Ø​, then we'll get set A

A U Ø​ = A

Ø​ U A = A

In a sense, it's analogous to adding 0. So it's like saying A+0 = A and 0+A = A.

So that's why {6, 11, 15} U Ø​ = {6, 11, 15}

There's nothing to add onto the set {6, 11, 15}, so we just get the same thing back again.

If the confidence level will increase, the margin of error will also increases.

The margin of error is defined a range of values below and above the sample statistic in a confidence interval.

The confidence interval is a way to show what is uncertainty is with a certain statistic.

According to the given question

Environmentalist estimating true mean weight or all cars.

For the true mean weights of 2.8 to 3.4 tons the confidence level is 90%.

Since, the confidence level increases, the critical value increases and hence the margin of error increases.

Therefore, if the confidence level will increase, the margin of error will also increases.

Find out more information about confidence interval and margin error here:

https://brainly.com/question/15079850

#SPJ2

Answer:

I don't understand the question

Answer:

Volume = 18 cm^3

Surface Area = 58 cm^2

Step-by-step explanation:

Find the volume with the formula V=w*h*l

W= width

H = height

L = length

W= 2cm

H= 1 cm

L= 9 cm

V= w*h*l

V= 2cm * 1 cm * 9cm

V= 18 cm^3

Find the surface area with the formula A= 2(w*l + h*l + h* w)

W= width

H = height

L = length

W= 2cm

H= 1 cm

L= 9 cm

A= 2(w*l + h*l + h* w)

A= 2(2cm*9cm + 1cm*9cm + 1cm* 2cm)

A= 2(29cm)

A= 58cm^2

Answer:

6x

Step-by-step explanation:

If x is the length of one side, and each side is the same length, you will multiply it by 6 times (there are 6 sides in a hexagon).

So, you will add it up 6 times, but you can say 6x for short.

Answer:

(110.295, 122.093).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 12 - 1 = 11

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7959

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.7959\frac{11.3781}{\sqrt{12}} = 5.899[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 116.194 - 5.899 = 110.295

The upper end of the interval is the sample mean added to M. So it is 116.194 + 5.899 = 122.093

So

(110.295, 122.093).

Answer:

B

Step-by-step explanation:

because

Answer: 3 years

Step-by-step explanation:

Interest is calculated as:

= (P × R × T) / 100

where

P = principal = 150,000

R = rate = 2.5%.

I = interest = 11250

T = time = unknown.

I = (P × R × T) / 100

11250 = (150000 × 2.5 × T)/100

Cross multiply

1125000 = 375000T

T = 1125000/375000

T = 3

The time taken will be 3 years

Answer:

The answer to your question is given below.

Step-by-step explanation:

6x⁴ + 4x³ – 10x

The greatest common factor can be obtained as follow:

6x⁴ = 2 * 3 * x * x * x * x

4x³ = 2 * 2 * x * x * x

10x = 2 × 5 * x

Greatest common factor = 2 * x

= 2x

Thus, the expression 6x⁴ + 4x³ – 10x can be written as:

6x⁴ + 4x³ – 10x = 2x(3x³ + 2x² – 5)

Slope-intercept form:

y = x + 2

Point-slope form:

y − 5 = 1 ⋅ ( x − 3 )

I hope this is correct and helps!

Answer:

hello dude

x - 9 = - 12

x = 9 -12

x = -3

HAVE A NİCE NİGHT

Step-by-step explanation:

Greetings from Turkey

We have to,

find the required value of x.

Let's start,

→ x - 9 = -12

→ x = -12 + 9

→ x = -3

Thus, -3 is the value of x.

This question is incomplete, the complete question is;

A student bought a smart-watch that tracks the number of steps she walks throughout the day. The table shows the number of steps recorded (t) minutes after 3:00 pm on the first day she wore the watch.

t (min)       0          10          20         30         40

Steps   3,288    4,659    5,522    6,686    7,128

a) Find the slopes of the secant lines corresponding to the given intervals of t.

1) [ 0, 40 ]

11) [ 10, 20 ]

111) [ 20, 30 ]

b) Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part (a). (Round your answer to the nearest integer.)

Answer:

a)

1) for [ 0, 40 ], slope is 96

11) for [ 10, 20 ],  slope is 86.3

111) for  [ 20, 30 ], slope is 116.4

b) the student's walking pace is 101 per min

Step-by-step explanation:

Given the data in the question;

t (min)       0          10          20         30         40

Steps   3,288    4,659    5,522    6,686    7,128

SLOPE OF SECANT LINES

1) [ 0, 40 ]

slope =  ( 7,128 - 3,288 ) / ( 40 - 0

= 3840 / 40 = 96

Hence slope is 96

11)  [ 10, 20 ]

slope = ( 5,522 - 4,659 ) / ( 20 - 10 )

= 863 / 10 = 86.3

Hence slope is 86.3

111)  [ 20, 30 ]

slope = ( 6,686 - 5,522 ) / ( 30 - 20 )

= 1164 / 10 = 116.4

Hence slope is 116.4

b)

Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part .

Since this is recorded after 3:00 pm

{ 3:20 - 3:00 = 20 }

so t = 20 min

so by average;

we have ( [ 10, 20 ] + [ 20, 30 ] ) /2

⇒ ( 86.3 + 116.4 ) / 2

= 202.7 /2

= 101.35 ≈ 101

Therefore, the student's walking pace is 101 per minutes

Answer:

r = 4.1231055

Step-by-step explanation:

So to do this, you need to find the distance between the two points:

(-7,1) and (1,3).

To do this, the distance or diameter (d) is equal to:

d = sqrt ((x2-x1)^2 + (y2-y1)^2)

In this case:

d = sqrt( (1 - (-7))^2 + (3 - 1)^2 )

d = sqrt( 8^2 + 2^2)

d = sqrt( 64 + 4)

d = sqrt( 68 )

The radius is half of the diameter, so:

r = 1/2 * d

r = 1/2 * sqrt( 68 )

r~ 4.1231055

Answer:

They are going away from each other.

So add up their speed.

combined speed = x+x-16

=2x-16

Time = 2 hours

Distance = 400 miles

Distance = speed * time

(2x-16)* 2

4x-32=400

4x=400+32

4x=432

/12

x=108 mph west bound

east bound = 108 -16 = 92 mph

Answer:

C. 0.48

Step-by-step explanation:

Probability = number of required outcome

_______________________

number of possible outcome

= total volleyball game events

_______________________

total sophomore + junior

= 66/137

= 0.48

Answer: D) 0.31

Step-by-step explanation:

Let A denote the event that a person is a sophomore.

Let B denote the event that a person has attended volleyball game.

A∩B denote the event that a person is a sophomore and attend volleyball game.

Let P denote the probability of an event.

We are asked to find:

P(A∩B)

From the table provided to us we see that:

A∩B=42

Hence,

P(A∩B)=42/137=0.3065 which is approximately equal to 0.31. Therefore ur answer will be 0.31.